Mathematics · Quantitative Aptitude

Mensuration of Solids

194 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

What is the volume of a cylinder with radius (r) and height (h)?

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

The volume of a cylinder is given by (\pi r^2 h), where (r) is the radius of the base and (h) is the height of the cylinder.

Multiple choice

What is the surface area of a cylinder with radius (r) and height (h)?

  1. \(2\pi r h + 2\pi r^2\)
  2. \(\pi r h + 2\pi r^2\)
  3. \(2\pi r h + \pi r^2\)
  4. \(\pi r h + \pi r^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cylinder is given by (2\pi r h + 2\pi r^2), where (r) is the radius of the base and (h) is the height of the cylinder.

Multiple choice

What is the volume of a cone with radius (r) and height (h)?

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

The volume of a cone is given by (\frac{1}{3}\pi r^2 h), where (r) is the radius of the base and (h) is the height of the cone.

Multiple choice

What is the surface area of a cone with radius (r) and height (h)?

  1. \(\pi r h + \pi r^2\)
  2. \(2\pi r h + \pi r^2\)
  3. \(\pi r h + 2\pi r^2\)
  4. \(2\pi r h + 2\pi r^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cone is given by (\pi r h + \pi r^2), where (r) is the radius of the base and (h) is the height of the cone.

Multiple choice

A cylinder has a radius of (3) centimeters and a height of (8) centimeters. What is the volume of the cylinder?

  1. \(75.4\) cm³
  2. \(94.2\) cm³
  3. \(113.1\) cm³
  4. \(131.9\) cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder is given by (\pi r^2 h). Substituting (r = 3) cm and (h = 8) cm, we get (\pi (3)^2 (8) = 75.4) cm³.

Multiple choice

A cone has a radius of (4) centimeters and a height of (10) centimeters. What is the volume of the cone?

  1. \(33.5\) cm³
  2. \(54.9\) cm³
  3. \(76.4\) cm³
  4. \(97.8\) cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cone is given by (\frac{1}{3}\pi r^2 h). Substituting (r = 4) cm and (h = 10) cm, we get (\frac{1}{3}\pi (4)^2 (10) = 33.5) cm³.

Multiple choice

A cylinder has a surface area of (300) square centimeters. The radius of the base is (5) centimeters. What is the height of the cylinder?

  1. \(10\) cm
  2. \(12\) cm
  3. \(14\) cm
  4. \(16\) cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cylinder is given by (2\pi r h + 2\pi r^2). Solving for (h), we get (h = \frac{A - 2\pi r^2}{2\pi r}). Substituting (A = 300) cm², (r = 5) cm, and (\pi \approx 3.14), we get (h = \frac{300 - 2\pi (5)^2}{2\pi (5)} = 10) cm.

Multiple choice

What is the formula for calculating the volume of a cylinder?

  1. V = π * r^2 * h

  2. V = 2 * π * r * h

  3. V = π * r

  4. V = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the volume of a cylinder is V = π * r^2 * h, where r is the radius of the base and h is the height of the cylinder.

Multiple choice

What is the formula for calculating the volume of a cone?

  1. V = 1/3 * π * r^2 * h

  2. V = 2 * π * r * h

  3. V = π * r

  4. V = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the volume of a cone is V = 1/3 * π * r^2 * h, where r is the radius of the base and h is the height of the cone.

Multiple choice

What is the formula for calculating the surface area of a cylinder?

  1. SA = 2 * π * r * h + 2 * π * r^2

  2. SA = 2 * π * r * h

  3. SA = π * r

  4. SA = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the surface area of a cylinder is SA = 2 * π * r * h + 2 * π * r^2, where r is the radius of the base and h is the height of the cylinder.

Multiple choice

What is the formula for calculating the surface area of a cone?

  1. SA = π * r * l + π * r^2

  2. SA = 2 * π * r * h

  3. SA = π * r

  4. SA = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the surface area of a cone is SA = π * r * l + π * r^2, where r is the radius of the base, l is the slant height, and h is the height of the cone.

Multiple choice

What is the formula for calculating the lateral surface area of a cylinder?

  1. LSA = 2 * π * r * h

  2. LSA = 2 * π * r * h + 2 * π * r^2

  3. LSA = π * r

  4. LSA = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the lateral surface area of a cylinder is LSA = 2 * π * r * h, where r is the radius of the base and h is the height of the cylinder.

Multiple choice

What is the formula for calculating the lateral surface area of a cone?

  1. LSA = π * r * l

  2. LSA = 2 * π * r * h

  3. LSA = π * r

  4. LSA = 2 * π * r^2 * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the lateral surface area of a cone is LSA = π * r * l, where r is the radius of the base and l is the slant height of the cone.

Multiple choice

Find the volume of a cylinder with radius 5 cm and height 10 cm.

  1. 250 cm^3

  2. 314 cm^3

  3. 350 cm^3

  4. 400 cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cylinder is calculated using the formula: $$Volume = \pi r^2 h$$ Substituting the given radius and height, we get: $$Volume = \pi \times 5^2 \times 10$$ $$Volume = \pi \times 25 \times 10$$ $$Volume = 250 cm^3$$