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All questions of Mensuration for Civil Engineering (CE) Exam
Smallest side of a right angled triangle is 13 cm less than the side of a square of perimeter 72 cm. Second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm. What is the largest side of the right angled triangle?- a)20 cm
- b)12 cm
- c)10 cm
- d)13 cm
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Smallest side of a right angled triangle is 13 cm less than the side of a square of perimeter 72 cm. Second largest side of the right angled triangle is 2 cm less than the length of the rectangle of area 112 cm² and breadth 8 cm. What is the largest side of the right angled triangle?
a)
20 cm
b)
12 cm
c)
10 cm
d)
13 cm
e)
None of these
|
Rajeev Kumar answered |
Side of square = 72/4 = 18 cm
Smallest side of the right angled triangle = 18 – 13 = 5 cm
Length of rectangle = 112/8 = 14 cm
Second side of the right angled triangle = 14 – 2 = 12 cm
Hypotenuse of the right angled triangle = √(25 + 144) = 13cm
Smallest side of the right angled triangle = 18 – 13 = 5 cm
Length of rectangle = 112/8 = 14 cm
Second side of the right angled triangle = 14 – 2 = 12 cm
Hypotenuse of the right angled triangle = √(25 + 144) = 13cm
A hemispherical bowl of diameter 16cm is full of ice cream. Each student in a class is served exactly 4 scoops of ice cream. If the hemispherical scoop is having a radius of 2cm, then ice cream is served to how many students?- a)16
- b)32
- c)64
- d)128
- e)None
Correct answer is option 'A'. Can you explain this answer?
A hemispherical bowl of diameter 16cm is full of ice cream. Each student in a class is served exactly 4 scoops of ice cream. If the hemispherical scoop is having a radius of 2cm, then ice cream is served to how many students?
a)
16
b)
32
c)
64
d)
128
e)
None
|
|
Rajeev Kumar answered |
2/3*π*8³ = n*4*2/3*π*2³
n = 16
n = 16
A circular wire of radius 56 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is- a)70cm
- b)75cm
- c)80cm
- d)85cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
A circular wire of radius 56 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is
a)
70cm
b)
75cm
c)
80cm
d)
85cm
e)
None of these
|
Preeti Khanna answered |
The perimeter of the circle, that is, the rectangle is,
P=2πr = 2 * 22/7 * 56 =16×22 cm.
Let us assume the actual length and breadth of the rectangle be, 6xand 5x
So perimeter will be,
P=2(6x+5x)=22x
16×22=22x
X=16.
The smaller side or breadth =5x=80cm
P=2πr = 2 * 22/7 * 56 =16×22 cm.
Let us assume the actual length and breadth of the rectangle be, 6xand 5x
So perimeter will be,
P=2(6x+5x)=22x
16×22=22x
X=16.
The smaller side or breadth =5x=80cm
A well with 28 m inside diameter is dug out 18 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embarkment. Find the height of the embarkment.- a)3 m
- b)8 m
- c)9 m
- d)6 m
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
A well with 28 m inside diameter is dug out 18 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embarkment. Find the height of the embarkment.
a)
3 m
b)
8 m
c)
9 m
d)
6 m
e)
None of these
|
Anaya Patel answered |
22/7[(R2) – (r2)] * h = 22/7(7*7*18)
[(352) – (72)]h = 14 * 14 * 18
(42*28)h = 14*14*18
h = 3 m
[(352) – (72)]h = 14 * 14 * 18
(42*28)h = 14*14*18
h = 3 m
A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 18 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many cm will the water level rise?- a)10 cm
- b)18 cm
- c)12 cm
- d)16 cm
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 18 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many cm will the water level rise?
a)
10 cm
b)
18 cm
c)
12 cm
d)
16 cm
e)
None of these
|
|
Aarav Sharma answered |
Volume of the Rectangular Block = 22 * 18 * 7
Radius of the Cistern = 7 cm
Area of the Cylinder = Π * r� * h = 22/7 * 7 * 7 * h
22/7 * 7 * 7 * h = 22 * 18 * 7; h = 18 cm
A smaller triangle is having three sides. Another big triangle is having sides exactly double the sides of the smaller triangle. Then what is the ratio of Area of Smaller triangle to Area of the Bigger triangle?- a)1:2
- b)2:1
- c)1:4
- d)4:1
- e)Cannot be determined
Correct answer is option 'C'. Can you explain this answer?
A smaller triangle is having three sides. Another big triangle is having sides exactly double the sides of the smaller triangle. Then what is the ratio of Area of Smaller triangle to Area of the Bigger triangle?
a)
1:2
b)
2:1
c)
1:4
d)
4:1
e)
Cannot be determined
|
Cstoppers Instructors answered |
Smaller triangle sides = a, b, c
Area= √s(s-a) (s-b) (s-c);
s=a+b+c/2
= √(a+b+c)(b+c-a)(a+c- b)(a+b-c)/4
Bigger triangle =2a, 2b, 2c
Area = √(a+b+c)(b+c-a)(a+c- b)(a+b-c)
Ratio = 1:4
Area= √s(s-a) (s-b) (s-c);
s=a+b+c/2
= √(a+b+c)(b+c-a)(a+c- b)(a+b-c)/4
Bigger triangle =2a, 2b, 2c
Area = √(a+b+c)(b+c-a)(a+c- b)(a+b-c)
Ratio = 1:4
A hollow cylindrical tube is made of plastic is 4 cm thick. If the external diameter is 18 cm and length of the tube is 59cm, then find the volume of the plastic?- a)10380 cm³
- b)10384 cm³
- c)10440 cm³
- d)10444 cm³
- e)None
Correct answer is option 'B'. Can you explain this answer?
A hollow cylindrical tube is made of plastic is 4 cm thick. If the external diameter is 18 cm and length of the tube is 59cm, then find the volume of the plastic?
a)
10380 cm³
b)
10384 cm³
c)
10440 cm³
d)
10444 cm³
e)
None
|
|
Preeti Khanna answered |
R = 9, r =5
V =22/7*59(9 2 -5 2) = 10384
V =22/7*59(9 2 -5 2) = 10384
The area of the Circular garden is 88704 m². Outside the garden a road of 7m width laid around it. What would be the cost of laying road at Rs. 2/m².- a)Rs.7546
- b)Rs.10036
- c)Rs.11092
- d)Rs.15092
- e)Rs.16086
Correct answer is option 'D'. Can you explain this answer?
The area of the Circular garden is 88704 m². Outside the garden a road of 7m width laid around it. What would be the cost of laying road at Rs. 2/m².
a)
Rs.7546
b)
Rs.10036
c)
Rs.11092
d)
Rs.15092
e)
Rs.16086
|
KS Coaching Center answered |
88704 = 22/7*r
r =168
Outer radius = 168+7 = 175
Outer area = 22/7*175 2 = 96250
Road area = 96250 – 88704 = 7546
Cost = 7546*2 = 15092
r =168
Outer radius = 168+7 = 175
Outer area = 22/7*175 2 = 96250
Road area = 96250 – 88704 = 7546
Cost = 7546*2 = 15092
A room has floor size of 15*6sq cm. What is the height of the room , if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls ?- a)1.12cm
- b)3.24cm
- c)4.29cm
- d)2.5cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
A room has floor size of 15*6sq cm. What is the height of the room , if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls ?
a)
1.12cm
b)
3.24cm
c)
4.29cm
d)
2.5cm
e)
None of these
|
|
Rajeev Kumar answered |
lb+lb = lh+hb+lh+hb
2lb = 2h(l+b)
h = lb/l+b
h=15*6/15+6 = 4.29 cm
2lb = 2h(l+b)
h = lb/l+b
h=15*6/15+6 = 4.29 cm
A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?- a)15 minutes
- b)25 minutes
- c)35 minutes
- d)45 minutes
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time at the starting point, when both have started simultaneously from the same point in same direction?
a)
15 minutes
b)
25 minutes
c)
35 minutes
d)
45 minutes
e)
None of these
|
Shailendra Singh answered |
Time taken by a deer to complete one round = 9 minutes
Time taken by a rabbit to complete one round = 5 minutes
They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.
Time taken by a rabbit to complete one round = 5 minutes
They meet together for the first time at the starting point = LCM of 9 and 5 = 45 minutes.
The ratio between the sides of a room is 3:2. The cost of white washing the ceiling of the room at 5 Rs per square metre is Rs. 2500 and the cost of papering the walls at Rs. 2 per square metre is Rs. 960. The height of the room is?- a)4.8 m
- b)6.5 m
- c)3.5 m
- d)8.5 m
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
The ratio between the sides of a room is 3:2. The cost of white washing the ceiling of the room at 5 Rs per square metre is Rs. 2500 and the cost of papering the walls at Rs. 2 per square metre is Rs. 960. The height of the room is?
a)
4.8 m
b)
6.5 m
c)
3.5 m
d)
8.5 m
e)
None of these
|
|
Aryan Khanna answered |
Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 441 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?- a)354.5
- b)346.5
- c)316.5
- d)312.5
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
Circumference of a circle A is 22/7 times perimeter of a square. Area of the square is 441 cm². What is the area of another circle B whose diameter is half the radius of the circle A(in cm²)?
a)
354.5
b)
346.5
c)
316.5
d)
312.5
e)
None of the Above
|
|
Anshul Singh answered |
Area of square=441 cm2
i.e. (side)2=441 cm2
side=21cm
Circumference of circle A=2πr
Perimeter of square(p)=4*side=(4*21)cm=84cm
According to question,
Circumference of A=22/7 of p
i.e. 2πr=(22/7)*84
2(22/7)*r=(22/7)*84
2r=84
r=42cm
let radius of B be 'R',
Diameter of B=(1/2) of radius of A
Diameter of B=(1/2)*42=21cm
R=(21/2)cm
Area of Circle B=πR2
=(22/7)*(21/2)*(21/2)cm2
hence on calculating the above solution we
get that area of circle B=346.5
i.e. option b).
thanking you if you understand it so plzzz follow me.
i.e. (side)2=441 cm2
side=21cm
Circumference of circle A=2πr
Perimeter of square(p)=4*side=(4*21)cm=84cm
According to question,
Circumference of A=22/7 of p
i.e. 2πr=(22/7)*84
2(22/7)*r=(22/7)*84
2r=84
r=42cm
let radius of B be 'R',
Diameter of B=(1/2) of radius of A
Diameter of B=(1/2)*42=21cm
R=(21/2)cm
Area of Circle B=πR2
=(22/7)*(21/2)*(21/2)cm2
hence on calculating the above solution we
get that area of circle B=346.5
i.e. option b).
thanking you if you understand it so plzzz follow me.
A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?- a)65
- b)78
- c)82
- d)89
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?
a)
65
b)
78
c)
82
d)
89
e)
None of the Above
|
Kavya Saxena answered |
L = 30; lb = 720;
B= 24 ft
Length of fencing = l + 2b = 30 + 48 = 78 ft
B= 24 ft
Length of fencing = l + 2b = 30 + 48 = 78 ft
One of the adjacent sides of a rectangular courtyard is 5m and its diagonal measures 13 m long. What is the area of the courtyard?- a)60m²
- b)40m²
- c)50m²
- d)30m²
- e)None of the Above
Correct answer is option 'A'. Can you explain this answer?
One of the adjacent sides of a rectangular courtyard is 5m and its diagonal measures 13 m long. What is the area of the courtyard?
a)
60m²
b)
40m²
c)
50m²
d)
30m²
e)
None of the Above
|
|
Ravi Singh answered |
Another side = √[(13)² – (5)²] = 12m
Area = 12 * 5 = 60m²
Area = 12 * 5 = 60m²
The area of a rectangle is equal to the area of a square whose diagonal is 12√2 metre. The difference between the length and the breadth of the rectangle is 7 metre. What is the perimeter of rectangle ? (in metre).- a)68 metre
- b)50 metre
- c)62 metre
- d)64 metre
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
The area of a rectangle is equal to the area of a square whose diagonal is 12√2 metre. The difference between the length and the breadth of the rectangle is 7 metre. What is the perimeter of rectangle ? (in metre).
a)
68 metre
b)
50 metre
c)
62 metre
d)
64 metre
e)
None of the Above
|
|
Anaya Patel answered |
d = a√2
12√2 = a√2
a = 12
l * b = a² = (12²) = 144
l – b = 7 ; l = b + 7
(b + 7)*(b) = 144
b² + 7b – 144 = 0
b = 9; l = 16
2(l + b) = 2(16 + 9) = 50m
12√2 = a√2
a = 12
l * b = a² = (12²) = 144
l – b = 7 ; l = b + 7
(b + 7)*(b) = 144
b² + 7b – 144 = 0
b = 9; l = 16
2(l + b) = 2(16 + 9) = 50m
A right circular cone is placed over a cylinder of the same radius. Now the combined structure is painted on all sides. Then they are separated now the ratio of area painted on Cylinder to Cone is 3:1. What is the height of Cylinder if the height of Cone is 4 m and radius is 3 m?- a)5 m
- b)6 m
- c)8 m
- d)10 m
- e)Cannot be determined
Correct answer is 'B'. Can you explain this answer?
A right circular cone is placed over a cylinder of the same radius. Now the combined structure is painted on all sides. Then they are separated now the ratio of area painted on Cylinder to Cone is 3:1. What is the height of Cylinder if the height of Cone is 4 m and radius is 3 m?
a)
5 m
b)
6 m
c)
8 m
d)
10 m
e)
Cannot be determined
|
Naina Bansal answered |
Cylinder painted area = 2π rh+π r^2
Cone painted area = π rl
2h+r/√ (r^2 +h1^2 ) = 3:1
h = 6
The perimeter of a rectangle and a square is 80 cm each. If the difference between their areas is 100 cm. Find the sides of the rectangle.- a)30cm, 10cm
- b)40cm, 15cm
- c)25cm, 10cm
- d)20cm, 30cm
- e)None of the Above
Correct answer is option 'A'. Can you explain this answer?
The perimeter of a rectangle and a square is 80 cm each. If the difference between their areas is 100 cm. Find the sides of the rectangle.
a)
30cm, 10cm
b)
40cm, 15cm
c)
25cm, 10cm
d)
20cm, 30cm
e)
None of the Above
|
|
Hasan Jawad answered |
Non of the above
The biggest possible circle is inscribed in rectangle of length 10 m and breadth 7 m. Then the area of circle is?- a)35.8 m2
- b)36.5 m2
- c)30.5 m2
- d)38.5 m2
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
The biggest possible circle is inscribed in rectangle of length 10 m and breadth 7 m. Then the area of circle is?
a)
35.8 m2
b)
36.5 m2
c)
30.5 m2
d)
38.5 m2
e)
None of these
|
|
Preeti Khanna answered |
Radius = Breadth /2 = 7/2 = 3.5
Area = 22*3.5*3.5/7 = 269.5/7 = 38.5 m2
Area = 22*3.5*3.5/7 = 269.5/7 = 38.5 m2
If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?- a)990m²
- b)900m²
- c)930m²
- d)945m²
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
If each side pair of opposite sides of a square is increased by 20 m, the ratio of the length and breadth of the rectangular so formed becomes 5:3. The area of the old square is?
a)
990m²
b)
900m²
c)
930m²
d)
945m²
e)
None of the Above
|
Ankur Mathur answered |
Let the side of squares be x sq unit.
therefore as a pair opposite side increased by 20 units, hence now the rectangle obtained is of dimension-:
x, (x+20)
also the ration of sides is 5:3
so,
(x+20/x)= 5/3
solving this you will get X=30
hence the dimension of the square was of 30*30
hence area was 900sq unit.
therefore as a pair opposite side increased by 20 units, hence now the rectangle obtained is of dimension-:
x, (x+20)
also the ration of sides is 5:3
so,
(x+20/x)= 5/3
solving this you will get X=30
hence the dimension of the square was of 30*30
hence area was 900sq unit.
The length of a rectangle wall is 3/2 times of its height. If the area of the wall is 600m². What is the sum of the length and height of the wall?- a)40
- b)60
- c)50
- d)70
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
The length of a rectangle wall is 3/2 times of its height. If the area of the wall is 600m². What is the sum of the length and height of the wall?
a)
40
b)
60
c)
50
d)
70
e)
None of the Above
|
Akash Pandey answered |
length = 2x
height = 3x
Area of the wall = 3x * 2x = 6x² = 600
x = 10; Sum of the length and height of the wall = 50
height = 3x
Area of the wall = 3x * 2x = 6x² = 600
x = 10; Sum of the length and height of the wall = 50
What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?- a)27m
- b)28m
- c)29m
- d)25m
- e)15m
Correct answer is option 'C'. Can you explain this answer?
What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?
a)
27m
b)
28m
c)
29m
d)
25m
e)
15m
|
|
Alok Verma answered |
πR² = πr1² + πr2²
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29
The length of a rectangle is 3/5th of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?- a)112 cm²
- b)149 cm²
- c)189 cm²
- d)Cannot be determined
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
The length of a rectangle is 3/5th of the side of a square. The radius of a circle is equal to side of the square. The circumference of the circle is 132 cm. What is the area of the rectangle, if the breadth of the rectangle is 15 cm?
a)
112 cm²
b)
149 cm²
c)
189 cm²
d)
Cannot be determined
e)
None of these
|
|
KS Coaching Center answered |
Circumference of the circle = 132
2πR = 132; R = 21 cm
Side of square = 21 cm
Length of the rectangle = 3/5 * 21 = 63/5
Area of the rectangle = 63/5 * 15 = 189 cm²
2πR = 132; R = 21 cm
Side of square = 21 cm
Length of the rectangle = 3/5 * 21 = 63/5
Area of the rectangle = 63/5 * 15 = 189 cm²
The width of a rectangular piece of land is 1/4 th of its length. If the perimeter of the piece of land is 320 m its length is?- a)140 m
- b)128 m
- c)120 m
- d)156 m
- e)124 m
Correct answer is option 'B'. Can you explain this answer?
The width of a rectangular piece of land is 1/4 th of its length. If the perimeter of the piece of land is 320 m its length is?
a)
140 m
b)
128 m
c)
120 m
d)
156 m
e)
124 m
|
Yash Patel answered |
length = l ; breadth = l/4
2(l + b) = 320
2(l + l/4) = 320
l = 320 * 4/10 = 128m
2(l + b) = 320
2(l + l/4) = 320
l = 320 * 4/10 = 128m
In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 3m their ratio becomes 10:7. The area of the original rectangle in m² is?- a)384
- b)486
- c)346
- d)476
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 3m their ratio becomes 10:7. The area of the original rectangle in m² is?
a)
384
b)
486
c)
346
d)
476
e)
None of the Above
|
|
Kavya Saxena answered |
[3x + 3 / 2x + 3] = 10/ 7
x = 9
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 81 = 486m²
x = 9
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 81 = 486m²
A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time, when both have started simultaneously from the same point in same direction(in min)?- a)15/4
- b)45/4
- c)35/4
- d)25/4
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
A deer and a rabbit can complete a full round on a circular track in 9 minutes and 5 minutes respectively. P, Q, R and S are the four consecutive points on the circular track which are equidistant from each other. P is opposite to R and Q is opposite to S. After how many minutes will they meet together for the first time, when both have started simultaneously from the same point in same direction(in min)?
a)
15/4
b)
45/4
c)
35/4
d)
25/4
e)
None of these
|
|
Kavya Saxena answered |
Circumference of the track = LCM of 9 and 5 = 45 m.
Ratio of time of deer and rabbit = 9 : 5
Ratio of speed of deer and rabbit = 5 : 9
Relative Speed = 4 m/min
They meet together for the first time at the starting point = 45/4 min
Ratio of time of deer and rabbit = 9 : 5
Ratio of speed of deer and rabbit = 5 : 9
Relative Speed = 4 m/min
They meet together for the first time at the starting point = 45/4 min
Smallest side of a right angled triangle is 6 cm less than the side of a square of perimeter 60 cm. Second largest side of the right angled triangle is 4 cm less than the length of rectangle of area 80 sq. cm and breadth 5 cm. What is the largest side of the right angled triangle?- a)10cm
- b)9cm
- c)12cm
- d)15cm
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
Smallest side of a right angled triangle is 6 cm less than the side of a square of perimeter 60 cm. Second largest side of the right angled triangle is 4 cm less than the length of rectangle of area 80 sq. cm and breadth 5 cm. What is the largest side of the right angled triangle?
a)
10cm
b)
9cm
c)
12cm
d)
15cm
e)
None of these
|
|
Yash Patel answered |
Side of 1st square = 60/4 = 15 cm.
Smallest side of right angled triangle= 15 −6 = 9 cm.
Length of 2nd rectangle = 80/5 = 16 cm.
Second largest side of the 1strectangle = 16−4 = 12 cm.
Largest side = hypotenuse=√92+122=15cm
Smallest side of right angled triangle= 15 −6 = 9 cm.
Length of 2nd rectangle = 80/5 = 16 cm.
Second largest side of the 1strectangle = 16−4 = 12 cm.
Largest side = hypotenuse=√92+122=15cm
The perimeter of a square is equal to twice the perimeter of a rectangle of length 10 cm and breadth 4 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square?- a)38 cm
- b)23 cm
- c)46 cm
- d)36 cm
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
The perimeter of a square is equal to twice the perimeter of a rectangle of length 10 cm and breadth 4 cm. What is the circumference of a semi-circle whose diameter is equal to the side of the square?
a)
38 cm
b)
23 cm
c)
46 cm
d)
36 cm
e)
None of these
|
Faizan Khan answered |
Perimeter of square = 2(l + b)
= 2 * 2(10 + 4) = 2 * 28 = 56 cm
Side of square = 56/4 = 14 cm
Radius of semi circle = 14/2 = 7cm
Circumference of the semi-circle = 22/7 * 7 + 14 = 36 cm
= 2 * 2(10 + 4) = 2 * 28 = 56 cm
Side of square = 56/4 = 14 cm
Radius of semi circle = 14/2 = 7cm
Circumference of the semi-circle = 22/7 * 7 + 14 = 36 cm
A cylindrical tub of radius 10 cm contains water up to a depth of 25cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 5cm. What is the radius of the iron ball(approximate) ?- a)19
- b)15
- c)14
- d)17
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
A cylindrical tub of radius 10 cm contains water up to a depth of 25cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 5cm. What is the radius of the iron ball(approximate) ?
a)
19
b)
15
c)
14
d)
17
e)
None of these
|
|
Nikita Singh answered |
Volume of the ball = volume of the raised water
4*22*r3 /3*7 = 22*100*5
r3 = 11000*3*7/88 = 2625
r = 13.79 or 14
4*22*r3 /3*7 = 22*100*5
r3 = 11000*3*7/88 = 2625
r = 13.79 or 14
If the radius of cylinder is doubled, but height is reduced by 50%. What is the percentage change in volume?- a)100%
- b)150%
- c)125%
- d)175%
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
If the radius of cylinder is doubled, but height is reduced by 50%. What is the percentage change in volume?
a)
100%
b)
150%
c)
125%
d)
175%
e)
None of these
|
|
Nikita Singh answered |
R1/R2 = R/2R & H1/H2 = H/H/2
Original Volume = πr²h
New Volume = π(2r)²h/2
Change in Volume = (2 – 1)/1 * 100 = 100
Original Volume = πr²h
New Volume = π(2r)²h/2
Change in Volume = (2 – 1)/1 * 100 = 100
If the side of the square is increased by 30%, then how much % does its area get increased?- a)59%
- b)69%
- c)79%
- d)49%
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
If the side of the square is increased by 30%, then how much % does its area get increased?
a)
59%
b)
69%
c)
79%
d)
49%
e)
None of these
|
|
Alok Verma answered |
Area of the plot = 1.3 * 1.3 = 1.69 = 69%
A cylindrical tank of diameter 14 cm is full of water. If 9 litres of water is drawn off, the water level in the tank will drop by- a)230.6 cm
- b)223.5 cm
- c)233.8 cm
- d)238.3 cm
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
A cylindrical tank of diameter 14 cm is full of water. If 9 litres of water is drawn off, the water level in the tank will drop by
a)
230.6 cm
b)
223.5 cm
c)
233.8 cm
d)
238.3 cm
e)
None of these
|
|
Yash Patel answered |
1 litres = 1000 cm
9 litres = 9000 cm
Volume of cylinder = πr2h
22/7*7*7*h = 11000
h = 9000*7*4/22*7*7 = 233.8 cm
9 litres = 9000 cm
Volume of cylinder = πr2h
22/7*7*7*h = 11000
h = 9000*7*4/22*7*7 = 233.8 cm
A rectangular ground 16m long and 10m breadth. It has a gravel path 2.5m wide all around it on the outside. What is the area of the path?- a)159 m²
- b)155 m²
- c)187 m²
- d)183 m²
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
A rectangular ground 16m long and 10m breadth. It has a gravel path 2.5m wide all around it on the outside. What is the area of the path?
a)
159 m²
b)
155 m²
c)
187 m²
d)
183 m²
e)
None of the Above
|
|
Nikita Singh answered |
Area of ground = 16 * 10 = 160
Total area (ground + path) = (16 + 5)*(10 + 5) = 315
Area of path = 315 – 160 = 155 m²
Total area (ground + path) = (16 + 5)*(10 + 5) = 315
Area of path = 315 – 160 = 155 m²
A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?- a)53500
- b)49500
- c)51500
- d)52500
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
A solid metallic cylinder of base radius 5 cm and height 7 cm is melted to form cones, each of height 1 cm and base radius 1 mm. Find the number of cones?
a)
53500
b)
49500
c)
51500
d)
52500
e)
None of these
|
|
Aarav Sharma answered |
To solve this problem, we need to find the number of cones that can be formed by melting a solid metallic cylinder.
Given:
Base radius of the cylinder = 5 cm
Height of the cylinder = 7 cm
Height of each cone = 1 cm
Base radius of each cone = 1 mm = 0.1 cm
We can start by finding the volume of the cylinder and the volume of each cone.
1. Volume of the cylinder:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the base radius and h is the height. In this case, the radius of the cylinder is 5 cm and the height is 7 cm.
So the volume of the cylinder is V_cylinder = π(5^2)(7) = 175π cm^3.
2. Volume of each cone:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the base radius and h is the height. In this case, the radius of each cone is 0.1 cm and the height is 1 cm.
So the volume of each cone is V_cone = (1/3)π(0.1^2)(1) = (1/300)π cm^3.
Next, we need to find the number of cones that can be formed by dividing the volume of the cylinder by the volume of each cone.
3. Number of cones:
Number of cones = V_cylinder / V_cone
Number of cones = (175π) / ((1/300)π) = 52500
Therefore, the number of cones that can be formed is 52500.
Hence, the correct answer is option D) 52500.
Given:
Base radius of the cylinder = 5 cm
Height of the cylinder = 7 cm
Height of each cone = 1 cm
Base radius of each cone = 1 mm = 0.1 cm
We can start by finding the volume of the cylinder and the volume of each cone.
1. Volume of the cylinder:
The volume of a cylinder can be calculated using the formula V = πr^2h, where r is the base radius and h is the height. In this case, the radius of the cylinder is 5 cm and the height is 7 cm.
So the volume of the cylinder is V_cylinder = π(5^2)(7) = 175π cm^3.
2. Volume of each cone:
The volume of a cone can be calculated using the formula V = (1/3)πr^2h, where r is the base radius and h is the height. In this case, the radius of each cone is 0.1 cm and the height is 1 cm.
So the volume of each cone is V_cone = (1/3)π(0.1^2)(1) = (1/300)π cm^3.
Next, we need to find the number of cones that can be formed by dividing the volume of the cylinder by the volume of each cone.
3. Number of cones:
Number of cones = V_cylinder / V_cone
Number of cones = (175π) / ((1/300)π) = 52500
Therefore, the number of cones that can be formed is 52500.
Hence, the correct answer is option D) 52500.
ABCD is a square of 20 m. What is the area of the least-sized square that can be inscribed in it with its vertices on the sides of ABCD?- a)120 m²
- b)100 m²
- c)200 m²
- d)250 m²
- e)None
Correct answer is option 'C'. Can you explain this answer?
ABCD is a square of 20 m. What is the area of the least-sized square that can be inscribed in it with its vertices on the sides of ABCD?
a)
120 m²
b)
100 m²
c)
200 m²
d)
250 m²
e)
None
|
Ishani Rane answered |
It touches on midpoints on the sides of the square ABCD:
Side= √(10^2 +10^2) = √200
So, Area = 200 m^2
One side of rectangular ground is 8m and its diagonal is 17m. Find the area of ground?- a)150
- b)140
- c)130
- d)120
- e)None of the Above
Correct answer is option 'D'. Can you explain this answer?
One side of rectangular ground is 8m and its diagonal is 17m. Find the area of ground?
a)
150
b)
140
c)
130
d)
120
e)
None of the Above
|
|
Alok Verma answered |
d = √(l² + b²)
17 = √(l² + 8²)
l² = 17² – 8² ⇒ l = 289 – 64 = 225
l = 15 Area = 15 * 8 = 120m²
17 = √(l² + 8²)
l² = 17² – 8² ⇒ l = 289 – 64 = 225
l = 15 Area = 15 * 8 = 120m²
The width of a rectangular piece of land is 1/3 rd of its length. If the perimeter of the piece of land is 320m its length is?- a)140 m
- b)128 m
- c)120 m
- d)156 m
- e)124 m
Correct answer is option 'C'. Can you explain this answer?
The width of a rectangular piece of land is 1/3 rd of its length. If the perimeter of the piece of land is 320m its length is?
a)
140 m
b)
128 m
c)
120 m
d)
156 m
e)
124 m
|
|
Aarav Sharma answered |
length = l ; breadth = l/3
2(l + b) = 320
2(l + l/3) = 320
l = 320 * 3/8 = 120m
The length of a rectangular plot is 10 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?- a)50
- b)55
- c)60
- d)65
- e)None of the Above
Correct answer is option 'B'. Can you explain this answer?
The length of a rectangular plot is 10 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
a)
50
b)
55
c)
60
d)
65
e)
None of the Above
|
|
Aarav Sharma answered |
Given:
- Length of the rectangular plot = breadth + 10
- Cost of fencing the plot = Rs. 5300
- Cost per meter of fencing = Rs. 26.50
To find:
Length of the plot in meters
Solution:
Let's assume the breadth of the rectangular plot to be 'x' meters.
According to the given information, the length of the rectangular plot is 10 meters more than its breadth.
So, the length of the plot = x + 10 meters.
Perimeter of the rectangular plot:
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + breadth)
In this case, the perimeter of the plot is equal to the cost of fencing.
So, 2(length + breadth) = Rs. 5300
Substituting the values of length and breadth, we get:
2(x + 10 + x) = 5300
Simplifying the equation:
2(2x + 10) = 5300
4x + 20 = 5300
4x = 5300 - 20
4x = 5280
x = 5280/4
x = 1320/1
x = 1320 meters
So, the breadth of the rectangular plot is 1320 meters.
Now, we can find the length of the plot:
Length = breadth + 10
Length = 1320 + 10
Length = 1330 meters
Therefore, the length of the plot is 1330 meters.
Answer:
The length of the plot is 55 meters. (Option B)
- Length of the rectangular plot = breadth + 10
- Cost of fencing the plot = Rs. 5300
- Cost per meter of fencing = Rs. 26.50
To find:
Length of the plot in meters
Solution:
Let's assume the breadth of the rectangular plot to be 'x' meters.
According to the given information, the length of the rectangular plot is 10 meters more than its breadth.
So, the length of the plot = x + 10 meters.
Perimeter of the rectangular plot:
The perimeter of a rectangle is given by the formula:
Perimeter = 2(length + breadth)
In this case, the perimeter of the plot is equal to the cost of fencing.
So, 2(length + breadth) = Rs. 5300
Substituting the values of length and breadth, we get:
2(x + 10 + x) = 5300
Simplifying the equation:
2(2x + 10) = 5300
4x + 20 = 5300
4x = 5300 - 20
4x = 5280
x = 5280/4
x = 1320/1
x = 1320 meters
So, the breadth of the rectangular plot is 1320 meters.
Now, we can find the length of the plot:
Length = breadth + 10
Length = 1320 + 10
Length = 1330 meters
Therefore, the length of the plot is 1330 meters.
Answer:
The length of the plot is 55 meters. (Option B)
Find the area of a white sheet required to prepare a cone with a height of 21cm amd the radius of 20cm.- a)3080 cm²
- b)2300 cm²
- c)3460 cm²
- d)3600 cm²
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
Find the area of a white sheet required to prepare a cone with a height of 21cm amd the radius of 20cm.
a)
3080 cm²
b)
2300 cm²
c)
3460 cm²
d)
3600 cm²
e)
None of these
|
|
Rajeev Kumar answered |
r = 20 ; h = 21
l = √(400 + 441) = 29 cm
Total surface area = πrl + πr² = πr(l + r) = 22/7 * 20(49) = 3080 cm²
l = √(400 + 441) = 29 cm
Total surface area = πrl + πr² = πr(l + r) = 22/7 * 20(49) = 3080 cm²
A ladder is resting with one end in contact with the top of the wall of height 15m and the other end of the ground is at a distance 8m from the wall. The length of the ladder is?- a)17m
- b)18m
- c)16m
- d)15m
- e)10m
Correct answer is option 'A'. Can you explain this answer?
A ladder is resting with one end in contact with the top of the wall of height 15m and the other end of the ground is at a distance 8m from the wall. The length of the ladder is?
a)
17m
b)
18m
c)
16m
d)
15m
e)
10m
|
|
Shailendra Singh answered |
Hypotenuse = √(base)² + (altitude)²
√(8)² + (15)² = √289 = 17m
√(8)² + (15)² = √289 = 17m
A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 25paise per sq. m, is:- a)212
- b)195
- c)186
- d)174
- e)None of the Above
Correct answer is option 'C'. Can you explain this answer?
A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 25paise per sq. m, is:
a)
212
b)
195
c)
186
d)
174
e)
None of the Above
|
|
Faizan Khan answered |
Area to be plastered = [2(l + b) x h] + (l x b)
Area= {[2(25 + 12) x 6] + (25 x 12)} = 744 m2
Cost of plastering = 744 * 25/100 = 186
Area= {[2(25 + 12) x 6] + (25 x 12)} = 744 m2
Cost of plastering = 744 * 25/100 = 186
A hollow cylindrical tube open at both ends is made of plastic 4 cm thick. If the external diameter be 54 cm and the length of the tube be 490 cm, find the volume of plastic.- a)320000 cm³
- b)340000 cm³
- c)306300 cm³
- d)308000 cm³
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
A hollow cylindrical tube open at both ends is made of plastic 4 cm thick. If the external diameter be 54 cm and the length of the tube be 490 cm, find the volume of plastic.
a)
320000 cm³
b)
340000 cm³
c)
306300 cm³
d)
308000 cm³
e)
None of these
|
|
Alok Verma answered |
External Radius = 27; Internal Radius = 23
Volume of Plastic =πh(R² – r²) = 22/7 * 490(27² – 23²) = 308000 cm³
Volume of Plastic =πh(R² – r²) = 22/7 * 490(27² – 23²) = 308000 cm³
A circular wire of diameter 42cm is folded in the shape of a rectangle whose sides are in the ratio 6:5. Find the ratio of the enclosed rectangle ?- a)1080cm2
- b)1181cm2
- c)1250cm2
- d)1800cm2
- e)None of these
Correct answer is option 'A'. Can you explain this answer?
A circular wire of diameter 42cm is folded in the shape of a rectangle whose sides are in the ratio 6:5. Find the ratio of the enclosed rectangle ?
a)
1080cm2
b)
1181cm2
c)
1250cm2
d)
1800cm2
e)
None of these
|
|
Faizan Khan answered |
Radius = 42/2 = 21cm
Circumference = 2*22*21/7 = 132cm
L:b = 6x:5x
Perimeter of the rectangle = 2(6x+5x) = 22x
22x = 132
X = 6
Area = 6x * 5x = 30x*x
=30*6*6 = 1080cm2
Circumference = 2*22*21/7 = 132cm
L:b = 6x:5x
Perimeter of the rectangle = 2(6x+5x) = 22x
22x = 132
X = 6
Area = 6x * 5x = 30x*x
=30*6*6 = 1080cm2
The diameter of Road Roller is 84 cm and its length is 150 cm. It takes 600 revolutions to level once on a particular road. Then what is the area of that road in m²?- a)2376
- b)2476
- c)2496
- d)2516
- e)None
Correct answer is option 'A'. Can you explain this answer?
The diameter of Road Roller is 84 cm and its length is 150 cm. It takes 600 revolutions to level once on a particular road. Then what is the area of that road in m²?
a)
2376
b)
2476
c)
2496
d)
2516
e)
None
|
|
Ravi Singh answered |
600*2*22/7*42/100*150/100=2376
The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm. Find the area of the rectangle.- a)800 cm²
- b)500 cm²
- c)1000 cm²
- d)600 cm²
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
The perimeter of a rectangle and a square is 160 cm each. If the difference between their areas is 600 cm. Find the area of the rectangle.
a)
800 cm²
b)
500 cm²
c)
1000 cm²
d)
600 cm²
e)
None of these
|
|
Anaya Patel answered |
Perimeter of rectangle = Perimeter of Square = 160
4a = 160 ⇒ a = 40
Area of square = 1600
1600 – lb = 600
lb = 1000 cm²
4a = 160 ⇒ a = 40
Area of square = 1600
1600 – lb = 600
lb = 1000 cm²
The length of a plot is four times its breath. A playground measuring 400 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?- a)20
- b)30
- c)60
- d)40
- e)80
Correct answer is option 'E'. Can you explain this answer?
The length of a plot is four times its breath. A playground measuring 400 square meters occupies one fourth of the total area of a plot. What is the length of the plot in meter.?
a)
20
b)
30
c)
60
d)
40
e)
80
|
|
Aarav Sharma answered |
To solve this problem, we need to use the given information to find the length of the plot. Let's break down the information step by step:
1. The length of a plot is four times its breadth: Let's assume the breadth of the plot is 'x'. According to the given information, the length of the plot would be 4x.
2. A playground occupies one fourth of the total area of the plot: The area of the playground is given as 400 square meters. Since the playground occupies one fourth of the total area of the plot, we can calculate the total area of the plot by multiplying the area of the playground by 4. So, the total area of the plot would be 400 * 4 = 1600 square meters.
3. Now, we can use the total area of the plot to find the length. The formula to calculate the area of a rectangle is length * breadth. We know that the area of the plot is 1600 square meters and the length is 4x. Substituting these values into the formula, we get:
4x * x = 1600
4. Simplifying the equation, we have:
4x^2 = 1600
5. Dividing both sides of the equation by 4, we get:
x^2 = 400
6. Taking the square root of both sides, we get:
x = √400
7. Simplifying the square root, we have:
x = 20
8. Since the length of the plot is four times its breadth, we have:
Length = 4x = 4 * 20 = 80 meters
Therefore, the length of the plot is 80 meters. The correct answer is option E.
1. The length of a plot is four times its breadth: Let's assume the breadth of the plot is 'x'. According to the given information, the length of the plot would be 4x.
2. A playground occupies one fourth of the total area of the plot: The area of the playground is given as 400 square meters. Since the playground occupies one fourth of the total area of the plot, we can calculate the total area of the plot by multiplying the area of the playground by 4. So, the total area of the plot would be 400 * 4 = 1600 square meters.
3. Now, we can use the total area of the plot to find the length. The formula to calculate the area of a rectangle is length * breadth. We know that the area of the plot is 1600 square meters and the length is 4x. Substituting these values into the formula, we get:
4x * x = 1600
4. Simplifying the equation, we have:
4x^2 = 1600
5. Dividing both sides of the equation by 4, we get:
x^2 = 400
6. Taking the square root of both sides, we get:
x = √400
7. Simplifying the square root, we have:
x = 20
8. Since the length of the plot is four times its breadth, we have:
Length = 4x = 4 * 20 = 80 meters
Therefore, the length of the plot is 80 meters. The correct answer is option E.
The length of a park is four times of its breadth. A playground whose area is 1600 m² covers 1/4th part of the park. The length of the park is?- a)108 m
- b)140 m
- c)120 m
- d)160 m
- e)180 m
Correct answer is option 'D'. Can you explain this answer?
The length of a park is four times of its breadth. A playground whose area is 1600 m² covers 1/4th part of the park. The length of the park is?
a)
108 m
b)
140 m
c)
120 m
d)
160 m
e)
180 m
|
Sagar Sharma answered |
The area of a rectangle is given by the formula A = length * breadth.
Let's assume the breadth of the park is x meters.
According to the problem, the length of the park is four times its breadth, so the length is 4x meters.
The area of the park is given as 1600 square meters, so we can write the equation:
1600 = 4x * x
Simplifying the equation:
1600 = 4x^2
Dividing both sides by 4:
400 = x^2
Taking the square root of both sides:
x = ±20
Since the breadth cannot be negative, we take the positive value:
x = 20 meters
Therefore, the breadth of the park is 20 meters and the length is 4 times the breadth, which is 4*20 = 80 meters.
Let's assume the breadth of the park is x meters.
According to the problem, the length of the park is four times its breadth, so the length is 4x meters.
The area of the park is given as 1600 square meters, so we can write the equation:
1600 = 4x * x
Simplifying the equation:
1600 = 4x^2
Dividing both sides by 4:
400 = x^2
Taking the square root of both sides:
x = ±20
Since the breadth cannot be negative, we take the positive value:
x = 20 meters
Therefore, the breadth of the park is 20 meters and the length is 4 times the breadth, which is 4*20 = 80 meters.
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