Volume of Solids

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Q. A cube has a side length of 4 cm. What is its volume?

A. 16 cm³
B. 32 cm³
C. 64 cm³
D. 48 cm³

Solution

Volume = s³ = 4³ = 64 cm³.

Correct Answer: C — 64 cm³

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Q. A pyramid has a square base with a side length of 6 cm and a height of 9 cm. What is its volume?

A. 54 cm³
B. 72 cm³
C. 108 cm³
D. 36 cm³

Solution

Volume = (1/3) × base area × height = (1/3) × (6²) × 9 = 108 cm³.

Correct Answer: B — 72 cm³

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Q. Calculate the volume of a triangular prism with a base area of 10 cm² and a height of 8 cm.

A. 80 cm³
B. 40 cm³
C. 60 cm³
D. 20 cm³

Solution

Volume = base area × height = 10 × 8 = 80 cm³.

Correct Answer: A — 80 cm³

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Q. Find the volume of a sphere with a radius of 5 cm.

A. 33.51 cm³
B. 65.45 cm³
C. 523.60 cm³
D. 125.66 cm³

Solution

Volume = (4/3)πr³ = (4/3)π(5)³ = (500/3)π ≈ 523.60 cm³.

Correct Answer: C — 523.60 cm³

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Q. What is the volume of a cone with a radius of 2 cm and a height of 6 cm?

A. 8.38 cm³
B. 12.57 cm³
C. 25.13 cm³
D. 16.76 cm³

Solution

Volume = (1/3)πr²h = (1/3)π(2)²(6) = 8π/3 ≈ 25.13 cm³.

Correct Answer: A — 8.38 cm³

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Q. What is the volume of a frustum of a cone with a radius of 3 cm at the top, 5 cm at the bottom, and a height of 4 cm?

A. 40.84 cm³
B. 30.00 cm³
C. 50.24 cm³
D. 60.00 cm³

Solution

Volume = (1/3)πh(R² + Rr + r²) = (1/3)π(4)(5² + 5*3 + 3²) = (1/3)π(4)(25 + 15 + 9) = (1/3)π(4)(49) ≈ 40.84 cm³.

Correct Answer: A — 40.84 cm³

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Q. What is the volume of a hemisphere with a radius of 7 cm?

A. 143.67 cm³
B. 107.76 cm³
C. 153.94 cm³
D. 98.17 cm³

Solution

Volume = (2/3)πr³ = (2/3)π(7)³ = (686/3)π ≈ 143.67 cm³.

Correct Answer: A — 143.67 cm³

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Q. What is the volume of a rectangular prism with dimensions 3 cm, 4 cm, and 5 cm?

A. 60 cm³
B. 12 cm³
C. 15 cm³
D. 20 cm³

Solution

Volume = l × w × h = 3 × 4 × 5 = 60 cm³.

Correct Answer: A — 60 cm³

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