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 toy is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3 cm. The total height of the toy is 7 cm. What is the total area of the toy?

  1. 103.7 sq. cm

  2. 214.5 sq. cm

  3. 215.4 sq. cm

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The toy consists of a hemisphere (radius 3) and a cone (radius 3, height 7-3=4). Surface area = 2*pi*r^2 + pi*r*l, where l = sqrt(3^2 + 4^2) = 5. Area = 2*pi*9 + pi*3*5 = 18*pi + 15*pi = 33*pi. 33 * 3.14159 = 103.67, which rounds to 103.7.

Multiple choice

The ratio of lateral surface area and volume of a cylinder is 1 : 6. What is the value of its total surface area when the ratio of radius to height is 2 : 3?

  1. 2266.5 sq. in

  2. 2262.4 sq. in

  3. 2260.8 sq. in

  4. 2254.6 sq. in
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Lateral surface area is 2*pi*r*h and volume is pi*r^2*h. Ratio (2*pi*r*h) / (pi*r^2*h) = 2/r = 1/6, so r = 12. Given r/h = 2/3, h = 18. Total surface area = 2*pi*r*(r+h) = 2 * 3.1416 * 12 * (12+18) = 2261.95, which is closest to 2260.8.