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Mensuration - MCQ 1 - Railways MCQ

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20 Questions MCQ Test - Mensuration - MCQ 1

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Mensuration - MCQ 1 - Question 1

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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

Detailed Solution for Mensuration - MCQ 1 - Question 1

Cylinder painted area = 2πrh+πr²
Cone painted area = πrl
2h+r/√ (r² +h1² ) = 3:1
h = 6

Mensuration - MCQ 1 - Question 2

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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

Detailed Solution for Mensuration - MCQ 1 - Question 2

600*2*22/7*42/100*150/100=2376

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Mensuration - MCQ 1 - Question 3

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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

Detailed Solution for Mensuration - MCQ 1 - Question 3

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

Mensuration - MCQ 1 - Question 4

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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

Detailed Solution for Mensuration - MCQ 1 - Question 4

It touches on midpoints on the sides of the square ABCD
Side= √ (10² +10²) = √200
Area= 200 m²

Mensuration - MCQ 1 - Question 5

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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

Detailed Solution for Mensuration - MCQ 1 - Question 5

2/3*π*8³ = n*4*2/3*π*2³
n = 16

Mensuration - MCQ 1 - Question 6

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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

Detailed Solution for Mensuration - MCQ 1 - Question 6

R = 9, r =5
V =22/7*59(9 2 -5 2) = 10384

Mensuration - MCQ 1 - Question 7

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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

Detailed Solution for Mensuration - MCQ 1 - Question 7

πR² = πr1² + πr2²
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29

Mensuration - MCQ 1 - Question 8

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A well with 14 m diameter is dug up to 49 m deep. Now the soil taken out during dug is made into cubical blocks of 3.5m side each. Then how many such blocks were made?

A.
22
B.
44
C.
88
D.
176
E.
None

Detailed Solution for Mensuration - MCQ 1 - Question 8

22/7*7²*49 = n*(7/2)³
n =176

Mensuration - MCQ 1 - Question 9

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If the ratio of radius two Cylinders A and B are in the ratio of 2:1 and their heights are in the ratio of 2:1 respectively. The ratio of their total surface areas of Cylinder A to B is?

A.
2:1
B.
1:2
C.
1:4
D.
4:1
E.
Cannot be determined

Detailed Solution for Mensuration - MCQ 1 - Question 9

Cylinder A: 2πr1 (r1 + h1)
Cylinder B: 2πr2 (r2 + h2)
r 1 /r 2 = 2:1; h 1 /h 2 = 2:1
T A /T B = 2πr1 (r1 + h1)/ 2πr2 (r2 + h2)

Mensuration - MCQ 1 - Question 10

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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

Detailed Solution for Mensuration - MCQ 1 - Question 10

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

Mensuration - MCQ 1 - Question 11

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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

Detailed Solution for Mensuration - MCQ 1 - Question 11

Volume of the Rectangular Block = 22 * 18 * 7
Radius of the Cistern = 7 cm
Area of the Cylinder = π * r² * h = 22/7 * 7 * 7 * h
22/7 * 7 * 7 * h = 22 * 18 * 7; h = 18 cm

Mensuration - MCQ 1 - Question 12

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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

Detailed Solution for Mensuration - MCQ 1 - Question 12

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

Mensuration - MCQ 1 - Question 13

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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

Detailed Solution for Mensuration - MCQ 1 - Question 13

2(l + b) = 4a = 80
l + b = 40; a = 20 ⇒ a² = 400
a² – lb = 100; 400 – lb =100; lb = 300
(l – b)² = (l + b)² – 4lb
(l – b)² = 1600 – 1200; l – b = 20;

Mensuration - MCQ 1 - Question 14

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The length of a wall is 5/4 times of its height. If the area of wall will be 500m². What is the sum of the length and height of the wall?

A.
55m
B.
45m
C.
40m
D.
50m
E.
None of these

Detailed Solution for Mensuration - MCQ 1 - Question 14

l = 5x; h = 4x ; l * h = 500
20x² = 500 ; x = 5
l + h = 25 + 20 = 45m

Mensuration - MCQ 1 - Question 15

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A circular path runs round a circular garden. If the difference between the circumference of the outer circle and inner circle is 88m. Find the width of Path?

A.
14 m
B.
15 m
C.
18 m
D.
13 m
E.
None of the Above

Detailed Solution for Mensuration - MCQ 1 - Question 15

Width of the Road = R – r
2πR – 2πr = 88
R – r = 14 m

Mensuration - MCQ 1 - Question 16

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The radius of a circle is 4 m. What is the radius of another circle whose area is 16 times of that first?

A.
16 m
B.
64 m
C.
256 m
D.
400 m
E.
None of these

Detailed Solution for Mensuration - MCQ 1 - Question 16

Ratio of areas = (ratio of radii)²
16/1 = (ratio of radii)²
ratio of radii = 4/1
The required radius = 16 m

Mensuration - MCQ 1 - Question 17

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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

Detailed Solution for Mensuration - MCQ 1 - Question 17

πR² = πr1² + πr2²
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29

Mensuration - MCQ 1 - Question 18

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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

Detailed Solution for Mensuration - MCQ 1 - Question 18

r = 20 ; h = 21
l = √(400 + 441) = 29 cm
Total surface area = πrl + πr² = πr(l + r) = 22/7 * 20(49) = 3080 cm²

Mensuration - MCQ 1 - Question 19

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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.
308000 cm³
C.
306300 cm³
D.
340000 cm³
E.
None of these

Detailed Solution for Mensuration - MCQ 1 - Question 19

External Radius = 27; Internal Radius = 23
Volume of Plastic =πh(R² – r²) = 22/7 * 490(27² – 23²) = 308000 cm³

Mensuration - MCQ 1 - Question 20

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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

Detailed Solution for Mensuration - MCQ 1 - Question 20

Number of cones =Volume of Cylinder / Volume of one cone
= π*5*5*7 / (1/3π * 1/10 * 1/10 * 1)
= 52500

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