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

$27$ metal balls each of radius r are melted together to form one big sphere of radius R. Then the ratio of surface area of the big sphere to that of a ball is __________.
  1. $9:1$
  2. $3:2$
  3. $\sqrt{27}:\sqrt{5}$
  4. $\sqrt{3}:1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of 27 small spheres = Volume of 1 big sphere. 27 * (4/3 * pi * r^3) = 4/3 * pi * R^3. So R^3 = 27r^3, which means R = 3r. Surface area ratio = (4 * pi * R^2) / (4 * pi * r^2) = R^2 / r^2 = (3r)^2 / r^2 = 9/1.

Multiple choice

The radius of a cylindrical box is $8$ cm and the height is $3$cm. The number of inches that may be added to either the radius or the height to give the same non-zero increase in volume is:
  1. $1$
  2. $5\dfrac{1}{3}$

  3. any number

  4. non-existent

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

Let the increase be x. Equating the volume increases gives 3π(8 + x)^2 - 3π(8)^2 = 64πx, which simplifies to x(3x - 16) = 0. Since the increase is non-zero, x = 16/3 = 5 1/3.

Multiple choice

Increasing the radius of a cylinder by 6 units increases the volume by y cubic units. Increasing the altitude of the cylinders by 6 units also increases the volume by y cubic units. If the original altitude is 2, then the original radius is

  1. 2

  2. 4

  3. 6
  4. $6\pi$

  5. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Original volume V = pi * r^2 * h = 2 * pi * r^2. New volume 1: pi * (r+6)^2 * 2 = V + y. New volume 2: pi * r^2 * (2+6) = V + y. So, 2 * pi * (r^2 + 12r + 36) = 8 * pi * r^2. r^2 + 12r + 36 = 4r^2. 3r^2 - 12r - 36 = 0. r^2 - 4r - 12 = 0. (r-6)(r+2) = 0. r = 6.