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

From a solid right circular cylinder with height 4 cm and radius of the base 3 cm, a right circular cone of the same height and the same radius is drilled out. Find the volume of the remaining solid.
  1. $55.42$ $cm^3$
  2. $65.42$ $cm^3$
  3. $75.42$ $cm^3$
  4. $85.42$ $cm^3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 3^2 * 4 = 36pi. Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 3^2 * 4 = 12pi. Remaining volume = 36pi - 12pi = 24pi. 24 * 3.14159 = 75.398, which is approximately 75.42.

Multiple choice

The radius of right cylinder A is twice the radius of right cylinder B, and the height of cylinder B is twice the height of cylinder A. What is the ratio of the volume of cylinder A to the volume of cylinder B?
  1. $2$
  2. $4$
  3. $1$
  4. $3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h. Cylinder A: rA = 2rB, hA = hB/2. Volume A = pi * (2rB)^2 * (hB/2) = pi * 4rB^2 * hB/2 = 2 * pi * rB^2 * hB. Volume B = pi * rB^2 * hB. Ratio A/B = 2.

Multiple choice

A container with a rectangular base of length $4.4$ m and breadth $2$ m is used to collect rain water. The height of the water level in the container is $4$ cm and water is transferred into a cylinder vessel with radius $40\ cm$. What will be the height of water level in the cylinder?
  1. $60$ cm
  2. $70$ cm
  3. $75$ cm
  4. $80$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of water = 4.4m * 2m * 0.04m = 0.352 m^3 = 352000 cm^3. Cylinder volume = pi * r^2 * h = pi * 40^2 * h = 352000. h = 352000 / (pi * 1600) = 220 / pi approx 70.02 cm.

Multiple choice

Lateral surface area of the frustum of a cone is
  1. $\pi (r_2 - r_1) h$
  2. $\pi (r_1 + r_2) h$
  3. $\pi (r_1 - r_2) l$
  4. $\pi (r_1 + r_2) l$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The lateral surface area of a frustum of a cone is given by the formula pi * (r1 + r2) * l, where r1 and r2 are the radii of the two bases and l is the slant height.

Multiple choice

A lead pencil is in the shape of a cylinder. The pencil is $21 cm$ long with radius $0.4 cm$ and its lead is of radius $0.1 cm$. What is the volume of wood in the pencil?
  1. $9.9 cm^{3}$
  2. $8.9cm^3$
  3. $7.8 cm^3$
  4. $8.5 cm^3$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of wood is the volume of the cylinder with radius 0.4 cm minus the volume of the lead cylinder with radius 0.1 cm. Volume = pi * h * (R^2 - r^2) = (22/7) * 21 * (0.4^2 - 0.1^2) = 66 * (0.16 - 0.01) = 66 * 0.15 = 9.9 cubic cm.