Quantitative Aptitude

Mensuration of Solid Figures

147 Questions

Mensuration of solid figures deals with calculating the volume and surface area of 3D shapes. Common structures include cubes, cuboids, and rectangular prisms. These quantitative aptitude questions are standard in SSC, banking, and railway recruitment tests.

Cube volume formulasCuboid surface areaRectangular prismsDensity calculationsDimensional ratios

Mensuration of Solid Figures Questions

Multiple choice

What is the volume of a pyramid with square base side length 10 cm and height 14 cm?

  1. 560 cm³

  2. 1120 cm³

  3. 1680 cm³

  4. 2240 cm³
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of a pyramid with square base is given by the formula V = (1/3)Bh, where B is the area of the base and h is the height of the pyramid. The area of a square is given by the formula A = s², where s is the length of a side. Therefore, the volume of a pyramid with square base side length 10 cm and height 14 cm is (1/3)(10²)(14) = 1120 cm³.

Multiple choice

What is the volume of a cube with side length 4 cm?

  1. 64 cm^3

  2. 128 cm^3

  3. 192 cm^3

  4. 256 cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube is given by the formula s^3, where s is the side length. Therefore, the volume of a cube with side length 4 cm is 4^3 = 64 cm^3.

Multiple choice

What is the volume of the Great Pyramid of Giza?

  1. 2,583,283 cubic meters

  2. 2,593,283 cubic meters

  3. 2,603,283 cubic meters

  4. 2,613,283 cubic meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of the Great Pyramid of Giza is 2,583,283 cubic meters (91,125,000 cubic feet). This is equivalent to the volume of about 1.3 million Volkswagen Beetles.

Multiple choice

What is the volume of a cube with side length (s)?

  1. \(s^2\)
  2. \(s^3\)
  3. \(2s^3\)
  4. \(4s^3\)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of a cube is given by (s^3), where (s) is the length of one side of the cube.

Multiple choice

What is the surface area of a cube with side length (s)?

  1. \(6s^2\)
  2. \(4s^2\)
  3. \(2s^2\)
  4. \(8s^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cube is given by (6s^2), where (s) is the length of one side of the cube.

Multiple choice

A cube has a volume of (64) cubic centimeters. What is the length of one side of the cube?

  1. \(2\) cm
  2. \(4\) cm
  3. \(6\) cm
  4. \(8\) cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Since the volume of a cube is (s^3), where (s) is the length of one side, we can solve for (s) by taking the cube root of the volume. (\sqrt[3]{64} = 4), so the length of one side of the cube is (4) cm.

Multiple choice

A cube has a surface area of (150) square centimeters. What is the length of one side of the cube?

  1. \(5\) cm
  2. \(6\) cm
  3. \(7\) cm
  4. \(8\) cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cube is given by (6s^2), where (s) is the length of one side. Solving for (s), we get (s = \sqrt{\frac{A}{6}}). Substituting (A = 150) cm², we get (s = \sqrt{\frac{150}{6}} = 5) cm.

Multiple choice

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

  1. V = s^3

  2. V = 2 * s^3

  3. V = 3 * s^3

  4. V = 4 * s^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the volume of a cube is V = s^3, where s is the length of the side of the cube.

Multiple choice

What is the formula for calculating the volume of a rectangular prism?

  1. V = l * w * h

  2. V = 2 * (l + w + h)

  3. V = l^2 * w * h

  4. V = 2 * l * w * h
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The formula for calculating the volume of a rectangular prism is V = l * w * h, where l is the length, w is the width, and h is the height of the prism.

Multiple choice

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

  1. SA = 6 * s^2

  2. SA = 2 * s^2

  3. SA = 3 * s^2

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

The formula for calculating the surface area of a cube is SA = 6 * s^2, where s is the length of the side of the cube.

Multiple choice

In the 2017 China Girls' Mathematical Olympiad, what was the volume of a cube with side length 5 cm?

  1. 125 cm^3

  2. 150 cm^3

  3. 175 cm^3

  4. 200 cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube with side length s is given by V = s^3. Plugging in the value s = 5, we get V = 5^3 = 125 cm^3.

Multiple choice

What is the volume of a cube with side length 4 cm?

  1. 64 cm^3

  2. 32 cm^3

  3. 16 cm^3

  4. 8 cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a cube is calculated by cubing its side length. Therefore, the volume of the given cube is: $$Volume = side^3$$ $$Volume = 4 cm^3$$ $$Volume = 64 cm^3$$