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 ratio of whole surface area of a certain cube is equal to the area of the curved surface area of a certain sphere. Then ratio of their volumes is
  1. $\pi:6$
  2. $\sqrt{\pi}:\sqrt{6}$
  3. $\sqrt{6}:\sqrt{\pi}$
  4. $6:\pi$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area of cube = 6a^2. Surface area of sphere = 4*pi*r^2. 6a^2 = 4*pi*r^2 => a^2/r^2 = 4*pi/6 = 2*pi/3. Ratio of volumes = a^3 / ((4/3)*pi*r^3) = (a/r)^3 * (3/(4*pi)). (a/r) = sqrt(2*pi/3). Ratio = (2*pi/3)^(3/2) * 3/(4*pi) = (2*pi/3) * sqrt(2*pi/3) * 3/(4*pi) = 0.5 * sqrt(2*pi/3) = sqrt( (1/4) * (2*pi/3) ) = sqrt(pi/6).

Multiple choice

The ratio of base radius and height of a cone is 3:4. IF the cost of smoothing the curved surface area at 5 rupees/sq. cm is Rs. 11550, then the volume of liquid in it is :
  1. $12936{ cm }^{ 3 }$
  2. $12693{ cm }^{ 3 }$
  3. $12653{ cm }^{ 3 }$
  4. $12542{ cm }^{ 3 }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Radius r = 3k, height h = 4k. Slant height l = 5k. Curved surface area = pi * r * l = pi * 3k * 5k = 15 * pi * k^2. Cost = 15 * pi * k^2 * 5 = 75 * pi * k^2 = 11550. k^2 = 11550 / (75 * pi) = 154 / pi. Volume = (1/3) * pi * r^2 * h = (1/3) * pi * (3k)^2 * (4k) = 12 * pi * k^3. This requires k, which is sqrt(154/pi). The calculation leads to approximately 12936.