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 right circular cylinder is to be made so that the sum of its radius and its height is 9 ft. The maximum volume of the cylinder can be

  1. 54 π ft3

  2. 108 π ft3

  3. 81π ft3

  4. 72 π ft3

  5. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let r be the radius and h be the height. We have r + h = 9, so h = 9 - r. The volume V = pi * r^2 * h = pi * r^2 * (9 - r) = pi * (9r^2 - r^3). Taking the derivative with respect to r and setting it to 0 gives 18r - 3r^2 = 0, so r = 6 and h = 3. The maximum volume is pi * 6^2 * 3 = 108pi.

Multiple choice

The cost of etching a glass with design varies directly as the square of its area. It will cost Rs. 16,200 to etch a glass plate of 1 m * 1 m dimensions. What would be the loss to an artist if he were to etch 6 pieces of dimensions 1/3 m * 1/3 m, instead of the 1 m * 1 m piece?

  1. 15,000

  2. 12,000

  3. 17,000

  4. 16,200
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Cost C = k * A^2. For 1m*1m, A=1, C=16200, so k=16200. For 6 pieces of (1/3)m*(1/3)m, area of one piece is 1/9. Cost per piece = 16200 * (1/9)^2 = 16200 / 81 = 200. Total cost for 6 pieces = 6 * 200 = 1200. Loss = 16200 - 1200 = 15000.