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

If the radius of a cylinder is increased by 25%, then by what percent must the height be reduced so that the volume of the cylinder remains the same?

  1. 36%

  2. 56%

  3. 64%

  4. 46%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume V = pi * r^2 * h. If r increases by 25%, the new radius is 1.25r. The new volume is pi * (1.25r)^2 * h_new = pi * 1.5625 * r^2 * h_new. For V to be constant, 1.5625 * h_new = h, so h_new = h / 1.5625 = 0.64h. The reduction is 1 - 0.64 = 0.36, or 36%.

Multiple choice

There is a circular field of area A square metres. A cylindrical ditch of radius 14 metres and depth 5 metres is dug on the same field, and the earth is taken out and spread over the remaining part of the circular field. The height of the field goes up by 0.55 metres. The value of A is

  1. 6216

  2. 4356

  3. 5216

  4. 6316

  5. 6116
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of earth taken out = pi * r^2 * depth = pi * 14^2 * 5 = 980 * pi. This volume is spread over the remaining area (A - pi * 14^2) to a height of 0.55m. So, 980 * pi = (A - 196 * pi) * 0.55. Solving for A gives A = 980 * pi / 0.55 + 196 * pi = 1781.8 * pi + 615.75 = 5600 + 615.75 = 6215.75, which rounds to 6216.

Multiple choice

A toy is in the shape of hemisphere mounted on a cone such that the radius of hemisphere is 21 cm. If the volume of the toy is 24024 cm3, then find the height of conical part of toy.

  1. 15 cm

  2. 12 cm

  3. 10 cm

  4. 22 cm

  5. 18 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * (22/7) * 21^3 = 19404. Volume of cone = 24024 - 19404 = 4620. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * (22/7) * 21^2 * h = 462 * h. So 462 * h = 4620, h = 10 cm.

Multiple choice

A right pyramid with a square base has side of base 12 cm and height 40 cm. It is kept on its base. It is cut into four parts of equal height by three cuts parallel to its base. What is the ratio of the volumes of the four parts?

  1. 1 : 8 : 27 : 70

  2. 1 : 7 : 19 : 47

  3. 1 : 7 : 19 : 37

  4. 1 : 8 : 27 : 64
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The pyramid is cut into 4 parts of equal height. The volumes of the pyramids formed by the top 1, 2, 3, and 4 sections follow the ratio of the cubes of their heights: 1^3 : 2^3 : 3^3 : 4^3 = 1 : 8 : 27 : 64. The volumes of the individual frustum parts are 1, (8-1)=7, (27-8)=19, and (64-27)=37.

Multiple choice

A hollow cylinder of thickness 0.7 cm and height 15 cm is made of iron. If the inner radius of the cylinder is 3.5 cm, then what is the total surface area (in cm2) of the hollow cylinder?

  1. 812.12

  2. 768.42

  3. 759.88

  4. 828.42
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Inner radius r = 3.5, thickness = 0.7, outer radius R = 4.2. Height h = 15. Total surface area = 2 * pi * R * h + 2 * pi * r * h + 2 * pi * (R^2 - r^2). Area = 2 * pi * 15 * (4.2 + 3.5) + 2 * pi * (17.64 - 12.25) = 2 * pi * 15 * 7.7 + 2 * pi * 5.39 = 231 * pi + 10.78 * pi = 241.78 * pi = 759.88.