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

In case of a right circular cylinder the radius of base and height are in the ratio $2:3$. Therefore, the ratio of lateral surface area to the total surface area is
  1. $5:3$
  2. $3:5$
  3. $2:5$
  4. $2:3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Radius r = 2k, height h = 3k. Lateral Surface Area (LSA) = 2 * pi * r * h = 2 * pi * (2k) * (3k) = 12 * pi * k^2. Total Surface Area (TSA) = LSA + 2 * pi * r^2 = 12 * pi * k^2 + 2 * pi * (2k)^2 = 12 * pi * k^2 + 8 * pi * k^2 = 20 * pi * k^2. Ratio LSA/TSA = 12/20 = 3/5.

Multiple choice

The surface area of a sphere of radius $5\space cm$ is five times the area of the curved surface of a cone of radius $4\space cm$. Find the height of the cone.
  1. $3\space cm$
  2. $2\space cm$
  3. $4\space cm$
  4. $5\space cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of a sphere is 4 * pi * r^2 = 4 * pi * 25 = 100 * pi. The curved surface area of a cone is pi * r * l = pi * 4 * l. Given 100 * pi = 5 * (pi * 4 * l), we get 100 = 20 * l, so l = 5. Using the Pythagorean theorem for the cone, h = sqrt(l^2 - r^2) = sqrt(5^2 - 4^2) = sqrt(25 - 16) = 3 cm.