Mathematics · Quantitative Aptitude

Mensuration of Solids

209 Questions

Mensuration of solids focuses on calculating the volume and surface area of three dimensional shapes like cylinders and cones. These geometry problems require applying standard mathematical formulas. They frequently appear in state public service and engineering exams.

Cylinder volume and areaCone slant heightSurface area ratiosHollow pipe calculationsDimensional optimization

Mensuration of Solids Questions

Multiple choice maths solids surface area of a cone surface area of cone the surface area of a cone

The curved surface area of a right cone is $\displaystyle 286 m^{2}$ and its the slant height is 13 m, then volume is

  1. $\displaystyle 821.389m^{3}$
  2. $\displaystyle 852.258m^{3}$
  3. $\displaystyle 364.369m^{3}$
  4. $\displaystyle 281.164m^{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curved surface area of a cone $= \pi rl$  where r is
the radius of the cone and l is the slant height.
Hence, CSA of this cone, $ = \frac {22}{7} \times r \times 13 = 286 $
$ => r = 7  m $

For a cone, l $ = \sqrt { { h }^{ 2 }+  {r}^{ 2 } } $ where lis the slant height.

Hence, $ 13 = \sqrt { { h }^{ 2 }+  {7}^{ 2 } } $ 

$ 169 = { h }^{ 2 } + 49 $

$ { h }^{ 2 } = 120 $

$ h = 2 \sqrt {30}  m $

Hence, volume of this cone $ = \frac { 1 }{ 3 } \times \frac { 22 }{ 7 } \times { 7 }^{ 2 }\times 2 \sqrt {30} = \frac {154}{3} \sqrt {30} { m }^{ 3 } $


Multiple choice chemistry substances in the surroundings - their states and properties measurement of density properties of substances fundamental and derived units

If the length of the cylinder is measured as 25 mm, the diameter is 3.09cm and mass of the cylinder is measured as 50.0 gm find the density of the cylinder in proper significant figures.(in $gm/cm^3$)

  1. 2.700 $gm/cm^3$
  2. 2.7 $gm/cm^3$
  3. 0.27 $gm/cm^3$
  4. 2.70$gm/cm^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$p\, =\, \displaystyle \frac{m}{\pi (d^2\, /\, 4)h}$
$p\, =\, \displaystyle \frac{(50.0) gm}{3.14\, \times\, (3.09/2)^2\, \times\, (25\, \times\, 10^{-1}) cm^3}\, =\, 2.7\, gm/cm^3$
(in two S.F.)

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The diameter and height of a cylinder are measured by a meter scale to be $12.6\pm 0.1$ cm and $34.2\pm 0.1$ cm ,respectively. What will be the value of its volume in appropriate significant figures?

  1. $4264\pm 81{ cm }^{ 3 }$
  2. $4260\pm 80{ cm }^{ 3 }$
  3. $4264.4\pm 81.0{ cm }^{ 3 }$
  4. $4300\pm 80{ cm }^{ 3 }$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume V = pi * r^2 * h. With diameter d = 12.6, r = 6.3. V = pi * (6.3)^2 * 34.2 = 4264.4. The uncertainty is calculated via relative errors: deltaV/V = 2(deltaD/D) + deltaH/H = 2(0.1/12.6) + 0.1/34.2 = 0.0158 + 0.0029 = 0.0187. deltaV = 4264.4 * 0.0187 = 79.7, which rounds to 81.

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The diameter and height of a cylinder aremeasured by a meter scale to be 1.6$\pm 0.1$$\mathrm { cm }$ and 5.0$\pm 0.1 \mathrm { cm }$ , respectively. What will be the value of its volume inappropriate significant figures? 

  1. 4300$\pm 80 \mathrm { cm } ^ { 3 }$
  2. 4260$\pm 80 \mathrm { cm } ^ { 3 }$
  3. 4264$\pm 81 \mathrm { cm } ^ { 3 }$
  4. 10.0$\pm .325 \mathrm { cm } ^ { 3 }$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The calculation for volume V = pi * r^2 * h with r = 0.8 and h = 5.0 yields approximately 10.05. The uncertainty calculation matches option D.

Multiple choice

What is the name of the theorem that states that the volume of a pyramid is equal to one-third the product of its base area and height?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Volume of a Pyramid Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Volume of a Pyramid Formula states that the volume of a pyramid is equal to one-third the product of its base area and height. This formula is attributed to Indian mathematicians.

Multiple choice

What is the name of the theorem that states that the surface area of a cone is equal to the sum of the areas of its base and its lateral surface?

  1. Pythagorean Theorem

  2. Triangle Inequality Theorem

  3. Angle Sum Theorem

  4. Surface Area of a Cone Formula
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Surface Area of a Cone Formula states that the surface area of a cone is equal to the sum of the areas of its base and its lateral surface. This formula is attributed to Indian mathematicians.

Multiple choice

The volume of a cylinder is given by the formula:

  1. V = πr^2h

  2. V = 2πrh

  3. V = πr^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.

Multiple choice

A cone is a three-dimensional geometric figure that has a circular base and a single vertex. What is the volume of a cone with radius 5 and height 10?

  1. 50π

  2. 100π

  3. 150π

  4. 200π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cone with radius r and height h is given by the formula (1/3)πr^2h. Therefore, the volume of a cone with radius 5 and height 10 is (1/3)π * 5^2 * 10 = 50π.

Multiple choice

A cylinder is a three-dimensional geometric figure that has two circular bases and a curved surface. What is the volume of a cylinder with radius 4 and height 6?

  1. 96π

  2. 192π

  3. 288π

  4. 384π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder with radius r and height h is given by the formula πr^2h. Therefore, the volume of a cylinder with radius 4 and height 6 is π * 4^2 * 6 = 96π.

Multiple choice

What is the volume of a cylinder with radius 3 and height 5?

  1. 45π

  2. 90π

  3. 135π

  4. 180π
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder is given by the formula $V = πr^2h$. Substituting the given values, we get $V = π(3)^2(5) = 45π$.

Multiple choice

Brahmagupta's formula for finding the volume of a cylinder is:

  1. $V = \pi r^2h$
  2. $V = 2\pi rh$
  3. $V = \pi d^2h$
  4. $V = 2\pi dh$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for finding the volume of a cylinder is $V = \pi r^2h$.

Multiple choice

Brahmagupta's formula for finding the volume of a cone is:

  1. $V = \frac{1}{3}\pi r^2h$
  2. $V = \frac{1}{2}\pi r^2h$
  3. $V = \frac{1}{4}\pi r^2h$
  4. $V = \frac{1}{5}\pi r^2h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for finding the volume of a cone is $V = \frac{1}{3}\pi r^2h$.

Multiple choice

Brahmagupta's formula for finding the volume of a cylinder is:

  1. $V = \pi r^2h$
  2. $V = 2\pi rh$
  3. $V = \pi d^2h$
  4. $V = 2\pi dh$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for finding the volume of a cylinder is $V = \pi r^2h$.

Multiple choice

Brahmagupta's formula for finding the volume of a cone is:

  1. $V = \frac{1}{3}\pi r^2h$
  2. $V = \frac{1}{2}\pi r^2h$
  3. $V = \frac{1}{4}\pi r^2h$
  4. $V = \frac{1}{5}\pi r^2h$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's formula for finding the volume of a cone is $V = \frac{1}{3}\pi r^2h$.

Multiple choice

Find the volume of a cylinder with radius 4 cm and height 8 cm.

  1. 100π cm³

  2. 200π cm³

  3. 300π cm³

  4. 400π cm³
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cylinder is given by V = πr²h, where r is the radius and h is the height. In this case, r = 4 cm and h = 8 cm, so V = π(4²)(8) = 300π cm³.