Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice

A solid cuboid has dimensions 14 cm × 18 cm × 24 cm. A hemisphere of radius 3.5 cm is cut from the centre of each face of cuboid. What is the total surface area (in cm2) of the remaining solid?

  1. 1902

  2. 1809

  3. 1706

  4. 2271
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Surface area of cuboid = 2(14*18 + 18*24 + 24*14) = 2(252 + 432 + 336) = 2040. Each hemisphere removed subtracts pi*r^2 from the surface but adds 2*pi*r^2 (the bowl surface), net change = +pi*r^2 per face. 6 faces, so 6 * pi * (3.5)^2 = 6 * (22/7) * 12.25 = 231. Total area = 2040 + 231 = 2271.

Multiple choice

A hemispherical dome is open from its base and is made of iron. The thickness of the dome is 3.5 m. The total cost of painting the dome's outer curved surface is Rs. 2464. If the rate of painting is Rs. 8 per m2, then what is the volume (in m3) of iron used in making dome?

  1. 656.42

  2. 614.21

  3. 524.46

  4. 628.83
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Outer surface area = 2464 / 8 = 308 m^2. 2 * pi * R^2 = 308. R^2 = 308 / (2 * 22/7) = 49. R = 7 m. Inner radius r = 7 - 3.5 = 3.5 m. Volume = (2/3) * pi * (R^3 - r^3) = (2/3) * (22/7) * (343 - 42.875) = (44/21) * 300.125 = 628.83 m^3.

Multiple choice

A cylinder of radius 4.5 cm and height 12 cm just fits in another cylinder completely with their axes perpendicular. What is the radius (in cm) of the second cylinder?

  1. 5

  2. 6

  3. 15

  4. 7.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For a cylinder of radius r and height h to fit inside another cylinder of radius R with axes perpendicular, the cross-section of the inner cylinder must fit within the circular cross-section of the outer cylinder. This requires the diagonal of the inner cylinder's rectangle (2r by h) to be less than or equal to the diameter of the outer cylinder (2R). Thus, sqrt((2*4.5)^2 + 12^2) = 2R. sqrt(9^2 + 12^2) = sqrt(81 + 144) = sqrt(225) = 15. So 2R = 15, R = 7.5.

Multiple choice

A cylindrical vessel contains 33,164 cubic centimetres of a liquid. The cost of painting its curved surface area at 2 paise/sq. cm is Rs. 95.04. Its approximate total surface area is

  1. 5724 cm2

  2. 5976 cm2

  3. 5742 cm2

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved surface area (CSA) = Cost / Rate = 95.04 / 0.02 = 4752 cm^2. Given volume V = 33164 = pi * r^2 * h and CSA = 2 * pi * r * h = 4752. Dividing V by CSA/2 gives r = 33164 / 2376 = 13.95, approx 14 cm. Then h = 4752 / (2 * pi * 14) approx 54 cm. Total surface area = CSA + 2 * pi * r^2 = 4752 + 2 * pi * 196 approx 4752 + 1231.5 = 5983.5 cm^2, which is closest to 5976.

Multiple choice

Two cylindrical tanks are placed side by side on a level surface. The first tank has a radius of 4 metres, a height of 10 metres and is full of water. The second tank has a radius of 6 metres, a height of 8 metres and is empty. Water is pumped from the first tank into the second until the depth of water in both the tanks is the same. The depth of water in each tank is approximately _________.

  1. 6.07 m

  2. 5.07 m

  3. 4.07 m

  4. 3.07 m

  5. 2.07 m
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total volume of water = pi * 4^2 * 10 = 160*pi. Total base area = pi * 4^2 + pi * 6^2 = 16*pi + 36*pi = 52*pi. Depth = Total Volume / Total Base Area = 160*pi / 52*pi = 160/52 = 40/13 = 3.0769... m.

Multiple choice

A solid cube of volume 13,824 cm3 is cut into 8 cubes of equal volumes. The ratio of the surface area of the original cube to the sum of the surface areas of three of the smaller cubes is:

  1. 2 : 3

  2. 4 : 3

  3. 8 : 3

  4. 2 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original volume = 13824, side = 24. Surface area = 6 * 24^2 = 3456. 8 smaller cubes, volume = 13824 / 8 = 1728. Side of small cube = 12. Surface area of one small cube = 6 * 12^2 = 864. Sum of surface areas of 3 small cubes = 3 * 864 = 2592. Ratio = 3456 / 2592 = 4 / 3.

Multiple choice

A rectangular paper of width 7 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder (in cubic cm).

  1. 8800 cubic cm

  2. 8600 cubic cm

  3. 8700 cubic cm

  4. 8900 cubic cm

  5. 8885 cubic cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a rectangular paper is rolled along its width, the width becomes the height of the cylinder, and the length becomes the circumference. However, the problem states the width is 7 cm and the cylinder radius is 20 cm. Volume = pi * r^2 * h = (22/7) * 20^2 * 7 = 22 * 400 = 8800.