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

A square sheet of side $28$ cm is folded into a cylinder by joining its two sides. Find the base area of the cylinder thus formed (in $\displaystyle cm^{2}$).
  1. $\displaystyle \frac{524}{11}$
  2. $\displaystyle \frac{575}{11}$
  3. $\displaystyle \frac{629}{11}$
  4. $\displaystyle \frac{686}{11}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Circumference of cylinder base = 28. 2 * pi * r = 28, so r = 14 / pi. Base area = pi * r^2 = pi * (14/pi)^2 = 196 / pi. Using pi = 22/7, area = 196 * 7 / 22 = 1372 / 22 = 686 / 11.

Multiple choice

A model of a building is in the from of a cone surmounting a cylinder. The radius of the cylinder is $6$ cm The height of the model is $\displaystyle 6\sqrt{3}$ cm. The vertical angle of the cone is $\displaystyle 120^{\circ}$. Find the volume of the model (in $\displaystyle cm^{2}$).
  1. $\displaystyle 148\sqrt{3}\pi $
  2. $\displaystyle 156\sqrt{3}\pi $
  3. $\displaystyle 162\sqrt{3}\pi $
  4. $\displaystyle 168\sqrt{3}\pi $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The cone has half-angle 60°, so its height is 6/tan(60°) = 2sqrt(3) cm. The cylinder height is 6sqrt(3) - 2sqrt(3) = 4sqrt(3) cm. Adding the cylinder and cone volumes gives 168sqrt(3)π cm^3.

Multiple choice

A right circular cone is inscribed in a hemisphere so that the base of the cone coincides with the base of the hemisphere. What is the ratio of the height of the cone to the radius of the hemisphere?
  1. $\sqrt {3} : 1$
  2. $1 : 1$
  3. $\dfrac {1}{2} : 1$
  4. $\sqrt {2} : 1$
  5. $2 : 1$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cone inscribed in a hemisphere, the height of the cone is equal to the radius of the hemisphere because the vertex of the cone touches the center of the hemisphere's base plane if inverted, or the height is simply r. The ratio is 1:1.

Multiple choice

If the height of cylinder becomes $4$ times of original height and radius is doubled, then which of following will be true?
  1. Volume of the cylinder will be $16$ times.

  2. volume of cylinder remain unchanged.

  3. Volume of cylinder will be halved.
  4. Volume of cylinder will be $\displaystyle\frac{1}{4}$ of original volume.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume = pi * r^2 * h. New volume = pi * (2r)^2 * (4h) = pi * 4r^2 * 4h = 16 * (pi * r^2 * h). The volume becomes 16 times the original.

Multiple choice

John built a rectangular cardboard box $25$ cm high with a square base and a volume of $2,500$ $\displaystyle { cm }^{ 3 }$. Then he realized he did not need a box that large, so he chopped off the height of the box reducing its volume to $1,000$ $\displaystyle { cm }^{ 3 }$. Was the new box cubical? Also, state its' height.
  1. $20cm$
  2. $10cm$
  3. $30cm$
  4. $40cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original box: Base area * height = 2500. Base area * 25 = 2500, so base area = 100. Since the base is square, side = 10. New box: Volume = 1000, Base area = 100 (remains the same). Height = 1000 / 100 = 10. Since height = side = 10, the new box is cubical.

Multiple choice

The diameter of a cylinder is $12$ m and its height is $10$ m. Find the curved surface area of a cylinder.
  1. $\displaystyle 240\pi { cm }^{ 2 }$
  2. $\displaystyle 120\pi { m }^{ 2 }$
  3. $\displaystyle 220\pi { m }^{ 2 }$
  4. $\displaystyle 230\pi { mm }^{ 2 }$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The curved surface area of a cylinder is calculated using the formula 2 * pi * r * h. Given the diameter is 12 m, the radius r is 6 m. Substituting the values, 2 * pi * 6 * 10 = 120 * pi m^2.

Multiple choice

The curved surface of a cylinder is $\displaystyle 1000{ \ mm }^{ 2 }$ and the radius is $20$ mm. Find height of the cylinder. (Round off the answer to nearest whole number).
  1. $\displaystyle 8{\  mm }$
  2. $\displaystyle 9{\  mm }$
  3. $\displaystyle 7.9{\  mm }$
  4. $\displaystyle 7.96{\  mm }$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved surface area of a cylinder = 2 * pi * r * h. 1000 = 2 * 3.14159 * 20 * h. 1000 = 125.66 * h. h = 1000 / 125.66 = 7.958. Rounding to the nearest whole number gives 8.