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

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.

Multiple choice

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

  1. 314 cm²

  2. 157 cm²

  3. 78.5 cm²

  4. 39.25 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cylinder is given by SA = 2πr(r + h), where r is the radius and h is the height. In this case, r = 5 cm and h = 10 cm, so SA = 2π(5)(5 + 10) = 314 cm².

Multiple choice

Find the volume of a cone with radius 3 cm and height 4 cm.

  1. 12π cm³

  2. 24π cm³

  3. 36π cm³

  4. 48π cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cone is given by V = ½πr²h, where r is the radius and h is the height. In this case, r = 3 cm and h = 4 cm, so V = ½π(3²)(4) = 12π cm³.

Multiple choice

Find the surface area of a cone with radius 6 cm and height 8 cm.

  1. 150.79 cm²

  2. 75.39 cm²

  3. 37.69 cm²

  4. 18.84 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cone is given by SA = πr(r + l), where r is the radius, l is the slant height, and h is the height. In this case, r = 6 cm and h = 8 cm. To find l, we use the Pythagorean theorem: l² = r² + h². Substituting the values, we get l² = 6² + 8² = 100. Therefore, l = 10 cm. Now we can calculate the surface area: SA = π(6)(6 + 10) = 150.79 cm².

Multiple choice

A cylinder has a radius of 6 cm and a height of 8 cm. What is the volume of the cylinder?

  1. 288π cm³

  2. 144π cm³

  3. 72π cm³

  4. 36π cm³
Reveal answer Fill a bubble to check yourself
A 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 = 6 cm and h = 8 cm, so V = π(6²)(8) = 288π cm³.

Multiple choice

A cone has a radius of 5 cm and a height of 12 cm. What is the volume of the cone?

  1. 314 cm³

  2. 157 cm³

  3. 78.5 cm³

  4. 39.25 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cone is given by V = ½πr²h, where r is the radius and h is the height. In this case, r = 5 cm and h = 12 cm, so V = ½π(5²)(12) = 314 cm³.

Multiple choice

A company wants to design a cylindrical can with a volume of 1000 cubic centimeters. What dimensions will minimize the surface area of the can?

  1. Radius: 5 cm, Height: 10 cm

  2. Radius: 6.32 cm, Height: 7.96 cm

  3. Radius: 7.07 cm, Height: 7.07 cm

  4. Radius: 8 cm, Height: 6.25 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using calculus, we can find the dimensions that minimize the surface area while satisfying the volume constraint.