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

The total surface area of a solid cube is 4.86 m2. It is melted and recast into a right circular cylinder of radius 0.3 m. What is the height (in m) of the cylinder (correct to one decimal place)? Take π = 22/7.

  1. 2.6

  2. 2.8

  3. 1.8

  4. 3.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of cube = 6a^2 = 4.86, so a^2 = 0.81, a = 0.9. Volume of cube = a^3 = 0.729. Volume of cylinder = pi * r^2 * h = (22/7) * (0.3)^2 * h = 0.729. h = (0.729 * 7) / (22 * 0.09) = 5.103 / 1.98 = 2.577, which rounds to 2.6.

Multiple choice

A solid metallic hemisphere of radius 6.3 cm is melted and recast into a right circular cylinder of radius 9 cm. What is the height (in cm, correct to one decimal place) of the cylinder?

  1. 1.9

  2. 2.1

  3. 2.7

  4. 2.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of hemisphere = (2/3) * pi * r^3 = (2/3) * pi * (6.3)^3. Volume of cylinder = pi * R^2 * h = pi * 9^2 * h. Equating them: (2/3) * (6.3)^3 = 81 * h. h = (2 * 250.047) / (3 * 81) = 500.094 / 243 = 2.058. Rounding to one decimal place gives 2.1.

Multiple choice

Column A Column B The volume of a rectangular solid with length 6 feet and a square base of side 4 The volume of a cylinder with a length of 7 feet and a diameter of 4 Compare the two quantities to decide whether

  1. the quantity in Column A is greater

  2. the quantity in Column B is greater

  3. the two quantities are equal

  4. the relationship cannot be determined from the information given
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The rectangular solid has volume 6 × 4^2 = 96 cubic feet. The cylinder has radius 2 feet and volume pi × 2^2 × 7 = 28pi, which is less than 96, so Column A is greater.