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 side length 4 cm.

  1. 96 cm²

  2. 48 cm²

  3. 32 cm²

  4. 16 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cube is given by SA = 6a², where a is the length of one side. In this case, a = 4 cm, so SA = 6(4²) = 96 cm².

Multiple choice

Find the volume of a rectangular prism with length 6 cm, width 4 cm, and height 3 cm.

  1. 72 cm³

  2. 24 cm³

  3. 18 cm³

  4. 12 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, l = 6 cm, w = 4 cm, and h = 3 cm, so V = 6 * 4 * 3 = 72 cm³.

Multiple choice

A rectangular prism has a length of 10 cm, a width of 5 cm, and a height of 3 cm. What is the volume of the prism?

  1. 150 cm³

  2. 75 cm³

  3. 37.5 cm³

  4. 18.75 cm³
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a rectangular prism is given by V = lwh, where l is the length, w is the width, and h is the height. In this case, l = 10 cm, w = 5 cm, and h = 3 cm, so V = 10 * 5 * 3 = 150 cm³.

Multiple choice

A cube has a side length of 7 cm. What is the surface area of the cube?

  1. 343 cm²

  2. 171.5 cm²

  3. 85.75 cm²

  4. 42.875 cm²
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cube is given by SA = 6a², where a is the length of one side. In this case, a = 7 cm, so SA = 6(7²) = 343 cm².

Multiple choice

What is the volume of a cube with side length 5 cm?

  1. 125 cm^3

  2. 250 cm^3

  3. 375 cm^3

  4. 500 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. Substituting s = 5 cm, we get (5)^3 = 125 cm^3.

Multiple choice

A company wants to produce a rectangular box with a square base and a volume of 1000 cubic centimeters. What dimensions will minimize the surface area of the box?

  1. 10 cm x 10 cm x 10 cm

  2. 12.5 cm x 12.5 cm x 6.67 cm

  3. 15 cm x 15 cm x 4.44 cm

  4. 20 cm x 20 cm x 2.5 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.

Multiple choice

A company wants to manufacture a rectangular box with an open top. The box must have a volume of 32 cubic feet. What dimensions will minimize the surface area of the box?

  1. Length: 4 feet, Width: 4 feet, Height: 2 feet

  2. Length: 6 feet, Width: 2 feet, Height: 2.67 feet

  3. Length: 8 feet, Width: 2 feet, Height: 2 feet

  4. Length: 10 feet, Width: 2 feet, Height: 1.6 feet
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.

Multiple choice

A company wants to design a rectangular box with a square base and a volume of 64 cubic inches. What dimensions will minimize the surface area of the box?

  1. 4 inches x 4 inches x 4 inches

  2. 6 inches x 6 inches x 3.5 inches

  3. 8 inches x 8 inches x 2 inches

  4. 10 inches x 10 inches x 1.6 inches
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.

Multiple choice

What is the value of the volume of a cube with a side length of 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 a side length of 5 cm is 125 cm^3.

Multiple choice

What is the value of the surface area of a cube with a side length of 5 cm?

  1. 150 cm^2

  2. 175 cm^2

  3. 200 cm^2

  4. 225 cm^2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The surface area of a cube with a side length of 5 cm is 150 cm^2.

Multiple choice

What is the volume of a cube with a side length of 5 cm?

  1. 125 cm^3

  2. 250 cm^3

  3. 375 cm^3

  4. 500 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 length of a side of the cube. In this case, s = 5 cm, so the volume is 5^3 = 125 cm^3.

Multiple choice

What is the volume of a cube with a side length of 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 calculated by cubing its side length. In this case, the side length is 4 cm, so the volume is 4 cm * 4 cm * 4 cm = 64 cm³.

Multiple choice

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

  1. 9 cm^3

  2. 18 cm^3

  3. 27 cm^3

  4. 36 cm^3
Reveal answer Fill a bubble to check yourself
C 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 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 V = s^3, where s is the side length of the cube. Therefore, the volume of a cube with side length 4 cm is 4^3 = 64 cm^3.

Multiple choice

Calculate the volume of a cube with side length 5 cm.

  1. 25 cm^3

  2. 50 cm^3

  3. 125 cm^3

  4. 250 cm^3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the volume of a cube, cube the side length: Volume = side length^3 = 5 cm^3 = 125 cm^3. Therefore, the answer is 125 cm^3.