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

Curved surface of the cylinder is ________.
  1. $\pi rl$
  2. $2\pi rh$
  3. $\pi { r }^{ 2 }h$
  4. $2\pi r(r+h)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The curved surface area of a cylinder is given by the circumference of the base multiplied by the height, which is 2 * pi * r * h.

Multiple choice

The height of a cone is $9 cm$ and the radius of the base is $7 cm$. The cone is melted and a cuboid is formed. The length of the base of the cuboid is $11 cm$ and breadth is $6 cm$. Find the height of the cuboid.
  1. $11cm$
  2. $9 cm$
  3. $7 cm$
  4. $5 cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 49 * 9 = 147 * pi. Volume of cuboid = l * b * h_cuboid = 11 * 6 * h_cuboid = 66 * h_cuboid. Equating volumes: 66 * h_cuboid = 147 * pi. Using pi approx 22/7, 66 * h_cuboid = 147 * (22/7) = 21 * 22 = 462. h_cuboid = 462 / 66 = 7 cm.

Multiple choice

The height and the radius of the base of a closed cylinder are in the ratio 3: 1. If its volume is 1029 $\displaystyle \pi:cm^{3};$ then its outer surface area is 526 $cm^2$

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume = pi * r^2 * h. Given h = 3r, Volume = pi * r^2 * (3r) = 3 * pi * r^3. 3 * pi * r^3 = 1029 * pi, so r^3 = 343, r = 7. Then h = 21. Surface area = 2 * pi * r * (r + h) = 2 * pi * 7 * (7 + 21) = 2 * pi * 7 * 28 = 392 * pi. 392 * pi is approx 1231.5, not 526.

Multiple choice

Find the volume and surface area of a sphere of radius $4.2$ cm. $\displaystyle \left [ \pi =\frac{22}{7} \right ]$
  1. $380.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
  2. $320.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
  3. $310.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
  4. $370.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume = (4/3) * pi * r^3 = (4/3) * (22/7) * (4.2)^3 = 310.464. Surface area = 4 * pi * r^2 = 4 * (22/7) * (4.2)^2 = 221.76.

Multiple choice

Find the volume of a sphere whose radius is $7\ cm$
  1. $1437\cfrac{1}{3}{cm}^{3}$
  2. $1437\cfrac{1}{4}{cm}^{3}$
  3. $1437\cfrac{2}{3}{cm}^{3}$
  4. $1437\cfrac{1}{2}{cm}^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = (4/3) * pi * r^3. Volume = (4/3) * (22/7) * 7 * 7 * 7 = (4/3) * 22 * 49 = 4312 / 3 = 1437.333 = 1437 1/3.