Mensuration - MCQ 3


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20 Questions MCQ Test Quantitative Aptitude for Competitive Examinations | Mensuration - MCQ 3

Mensuration - MCQ 3 for Quant 2022 is part of Quantitative Aptitude for Competitive Examinations preparation. The Mensuration - MCQ 3 questions and answers have been prepared according to the Quant exam syllabus.The Mensuration - MCQ 3 MCQs are made for Quant 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mensuration - MCQ 3 below.
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Mensuration - MCQ 3 - Question 1

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?

Detailed Solution for Mensuration - MCQ 3 - Question 1

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.

Mensuration - MCQ 3 - Question 2

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)?

Detailed Solution for Mensuration - MCQ 3 - Question 2

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

Mensuration - MCQ 3 - Question 3

A cylindrical cistern whose diameter is 14 cm is partly filled with water. If a rectangular block of iron 22 cm in length, 14 cm in breadth and 7 cm in thickness is wholly immersed in water, by how many centi metre will the water level rise?

Detailed Solution for Mensuration - MCQ 3 - Question 3

Volume of the block = 22 * 14 * 7
Radius of the cistern = 14/2 = 7
Volume of the Cylinder = 22/7 * R2 * h
22/7 * R2 * h = 22/7 * 7 * 7 * h
22/7 * 7 * 7 * h = 22 * 14 * 7 ⇒ h = 14

Mensuration - MCQ 3 - Question 4

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.

Detailed Solution for Mensuration - MCQ 3 - Question 4

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

Mensuration - MCQ 3 - Question 5

The radii of two cylinders are in the ratio 4:5 and their heights are in the ratio 5:7, What is the ratio of their curved surface areas?

Detailed Solution for Mensuration - MCQ 3 - Question 5

2πr1h1/2πr2h2= [4/5 * 5/7] = 4:7

Mensuration - MCQ 3 - Question 6

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?

Detailed Solution for Mensuration - MCQ 3 - Question 6

Area of Ceiling = Total Cost / Cost of 1 sq. Unit
= 2500/5 = 500
l:b = 2x:3x
l*b = 5x2 = 500
l = 30m & b = 20 m
Area of the 4 wall = 960/2 = 480
Height = 480 / 2(30 + 20) = 4.8m

Mensuration - MCQ 3 - Question 7

A park is in the form of a square one of whose sides is 50 m. The area of the park excluding the circular lawn in the centre of the park is 1884 m². The radius of the circular lawn is ?

Detailed Solution for Mensuration - MCQ 3 - Question 7

Area of park = 50 x 50 = 2500 m²
Area of circular lawn = Area of park – area of park excluding circular lawn
= 2500 – 1884
= 616
Area of circular lawn = (22/7) x r² = 616 m²
⇒ r² = (616 x 7) / 22
= 28 x 7
= 2 x 2 x 7 x 7
∴ r = 14 m

Mensuration - MCQ 3 - Question 8

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.

Detailed Solution for Mensuration - MCQ 3 - Question 8

Perimeter of rectangle = Perimeter of Square = 160
4a = 160 ⇒ a = 40
Area of square = 1600
1600 – lb = 600
lb = 1000 cm²

Mensuration - MCQ 3 - Question 9

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.?

Detailed Solution for Mensuration - MCQ 3 - Question 9

Area of the plot = (4 x 400) m²
= 1600 m²
Breadth = y meter
Length = 4y meter
Now area = 4y x y = 1600 m²
⇒ y² = 400 m²
⇒ y = 20 m
∴ Length of plot = 4y =80 m

Mensuration - MCQ 3 - Question 10

If the radius of the cone is doubled, keeping the height constant, what is the ratio of the volume of the smaller cone to larger cone?

Detailed Solution for Mensuration - MCQ 3 - Question 10

v1/v2 = (r1²) * h1 / (r2²) * h2 (h1=h2)
(r)²/(2r)²
v1/v2 = 1:4

Mensuration - MCQ 3 - Question 11

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 ?

Detailed Solution for Mensuration - MCQ 3 - Question 11

lb+lb = lh+hb+lh+hb
2lb = 2h(l+b)
h = lb/l+b
h=15*6/15+6 = 4.29 cm

Mensuration - MCQ 3 - Question 12

What is the volume of a right cone whose cross section is isosceles triangle with a base 10cm and slant height 13cm ?

Detailed Solution for Mensuration - MCQ 3 - Question 12

Base of the cone(r) =10/2 = 5 cm
Height of the cone (h)= √169-25 =√144 = 12
Volume = 1/3πr2 h
= 22*5*5*12/7*3 = 314.2 Sq cm

Mensuration - MCQ 3 - Question 13

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?

Detailed Solution for Mensuration - MCQ 3 - Question 13

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

Mensuration - MCQ 3 - Question 14

Circumference of a circle-A is 5/4 times perimeter of a square. Area of the square is 961 sq. cm. What is the area of another circle-B whose diameter is half the radius of the circle-A?

Detailed Solution for Mensuration - MCQ 3 - Question 14

The side of the square = a=√961=31 cm.
Perimeter = 4 X 31 = 124 cm The circumference of the circle = 5/4 x 124 = 22/7 x 2 x r
Radius = 155*7/44 = 24.6 cm
Half the radius of Circle-A = 12.3 cm.
Radius of Circle-B = 14/2 = 6.15 cm
The area = 22/7 x 6.15 x 6.15 = 54 cm2

Mensuration - MCQ 3 - Question 15

A horse is tethered to a peg with a 16 cm long rope at the corner of a 31 cm long and 27cm wide rectangular grass field. What area of the field will the horse graze?

Detailed Solution for Mensuration - MCQ 3 - Question 15

Area = [22*16*16/7] / 4
= 5632/7*4 = 201.1 cm2

Mensuration - MCQ 3 - Question 16

The biggest possible circle is inscribed in rectangle of length 10 m and breadth 7 m. Then the area of circle is?

Detailed Solution for Mensuration - MCQ 3 - Question 16

Radius = Breadth /2 = 7/2 = 3.5
Area = 22*3.5*3.5/7 = 269.5/7 = 38.5 m2

Mensuration - MCQ 3 - Question 17

In a swimming pool measuring 80 cm x 30 cm, 120 men take a dip. If the average displacement of water by a man is 5 cm cube, What will be the rise in water level ?

Detailed Solution for Mensuration - MCQ 3 - Question 17

Total volume displaced by 8 men= 120×5 cm cube
However volume=lxbxh=80x30xh
80x30xh=120×5
h=120*5/80*30 = 600/2400 = 0.25.
so the water level rises by 0.25 cm = ¼ cm

Mensuration - MCQ 3 - Question 18

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

Detailed Solution for Mensuration - MCQ 3 - Question 18

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

Mensuration - MCQ 3 - Question 19

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 ?

Detailed Solution for Mensuration - MCQ 3 - Question 19

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

Mensuration - MCQ 3 - Question 20

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) ?

Detailed Solution for Mensuration - MCQ 3 - Question 20

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

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