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

Find the surface area of a cube with a side length of 6 cm.

  1. 72 cm²

  2. 144 cm²

  3. 216 cm²

  4. 288 cm²
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The surface area of a cube is calculated by multiplying the area of one face by 6. In this case, the area of one face is 6 cm x 6 cm = 36 cm². Therefore, the surface area of the cube is 36 cm² x 6 = 216 cm².

Multiple choice

What is the volume of a cube with side length 3 cm?

  1. 9 cm^3

  2. 27 cm^3

  3. 81 cm^3

  4. 243 cm^3
Reveal answer Fill a bubble to check yourself
B 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 3 cm is (3)^3 = 27 cm^3.

Multiple choice

What is Brahmagupta's rule for finding the volume of a pyramid?

  1. The volume of a pyramid is equal to one-third the product of its base area and height.

  2. The volume of a pyramid is equal to half the product of its base area and height.

  3. The volume of a pyramid is equal to the product of its base area and height.

  4. The volume of a pyramid is equal to twice the product of its base area and height.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's rule for finding the volume of a pyramid states that the volume of a pyramid is equal to one-third the product of its base area and height.

Multiple choice

What is the formula for finding the volume of a cube with side (a)?

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

The formula for finding the volume of a cube with side (a) is (a^3).

Multiple choice

What is the formula for finding the surface area of a cube with side (a)?

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

The formula for finding the surface area of a cube with side (a) is (6a^2).

Multiple choice

The formula for calculating the volume of a cube is:

  1. V = s^3

  2. V = 2 * s^3

  3. V = (1/2) * 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 one side of the cube.

Multiple choice

The formula for calculating the volume of a pyramid is:

  1. V = (1/3) * B * h

  2. V = 2 * B * h

  3. V = 4 * B * h

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

The formula for calculating the volume of a pyramid is V = (1/3) * B * h, where B is the area of the base of the pyramid and h is the height of the pyramid.

Multiple choice

The formula for calculating the volume of a prism is:

  1. V = B * h

  2. V = 2 * B * h

  3. V = 4 * B * h

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

The formula for calculating the volume of a prism is V = B * h, where B is the area of the base of the prism and h is the height of the prism.

Multiple choice

Find the volume of a rectangular prism with a length of 10 cm, a width of 5 cm, and a height of 3 cm.

  1. 150 cm^3

  2. 200 cm^3

  3. 250 cm^3

  4. 300 cm^3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a rectangular prism is given by the formula V = l * w * h, where l is the length, w is the width, and h is the height. Substituting the given values, we get V = 10 cm * 5 cm * 3 cm = 150 cm^3.

Multiple choice

What is the approximate size of Wernicke's area?

  1. 10 cubic centimeters

  2. 20 cubic centimeters

  3. 30 cubic centimeters

  4. 40 cubic centimeters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Wernicke's area is approximately 20 cubic centimeters in size. It is located in the posterior superior temporal gyrus of the left hemisphere of the brain.

Multiple choice

What was the name of the ancient Egyptian unit of volume that was approximately equal to the volume of a cubic cubit?

  1. Hekat

  2. Deben

  3. Qat

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

The hekat was the primary unit of volume used by the ancient Egyptians and was approximately equal to the volume of a cubic cubit.

Multiple choice

What is the volume of a pyramid with base area (B) and height (h)?

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

The volume of a pyramid with base area (B) and height (h) is given by (\frac{1}{3}Bh).

Multiple choice

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

  1. $32$ cm$^3$
  2. $64$ cm$^3$
  3. $96$ cm$^3$
  4. $128$ cm$^3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of a cube is given by the formula $V = a^3$, where $a$ is the side length. Substituting the given value, we get $V = 4^3 = 64$ cm$^3$.

Multiple choice

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

  1. 16 cm³

  2. 32 cm³

  3. 64 cm³

  4. 128 cm³
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cube is given by the formula V = s³, where s is the length of a side. Therefore, the volume of a cube with side length 4 cm is 4³ = 64 cm³.

Multiple choice

What is the volume of a pyramid with square base side length 8 cm and height 12 cm?

  1. 256 cm³

  2. 512 cm³

  3. 768 cm³

  4. 1024 cm³
Reveal answer Fill a bubble to check yourself
A 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 8 cm and height 12 cm is (1/3)(8²)(12) = 256 cm³.