Visualising Solid Shapes

Q. A cone has a base radius of 2 cm and a height of 6 cm. What is its volume?

A. 8π cm³
B. 12π cm³
C. 4π cm³
D. 16π cm³

Solution

Volume of a cone = (1/3)πr²h = (1/3)π(2)²(6) = 8π cm³.

Correct Answer: B — 12π cm³

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

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

Solution

Volume of a cube = side³ = 4³ = 64 cm³.

Correct Answer: B — 64 cm³

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Q. A rectangular box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is its volume?

A. 100 cm³
B. 50 cm³
C. 20 cm³
D. 70 cm³

Solution

Volume = length × width × height = 10 × 5 × 2 = 100 cm³.

Correct Answer: A — 100 cm³

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Q. A rectangular prism has dimensions 2 cm, 3 cm, and 4 cm. What is its surface area?

A. 24 cm²
B. 28 cm²
C. 20 cm²
D. 18 cm²

Solution

Surface area = 2(lw + lh + wh) = 2(2*3 + 2*4 + 3*4) = 2(6 + 8 + 12) = 2(26) = 52 cm².

Correct Answer: A — 24 cm²

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Q. A triangular prism has a base area of 10 cm² and a height of 5 cm. What is its volume?

A. 25 cm³
B. 50 cm³
C. 15 cm³
D. 30 cm³

Solution

Volume = Base area × height = 10 cm² × 5 cm = 50 cm³.

Correct Answer: A — 25 cm³

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Q. If a cube's volume is 27 cm³, what is the length of one side?

A. 3 cm
B. 4 cm
C. 5 cm
D. 6 cm

Solution

Side length = ∛Volume = ∛27 = 3 cm.

Correct Answer: A — 3 cm

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Q. If a cylinder has a radius of 3 cm and a height of 5 cm, what is its volume?

A. 45π cm³
B. 30π cm³
C. 15π cm³
D. 60π cm³

Solution

Volume of a cylinder = πr²h = π(3)²(5) = 45π cm³.

Correct Answer: A — 45π cm³

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Q. What is the surface area of a cube with a side length of 3 cm?

A. 27 cm²
B. 36 cm²
C. 18 cm²
D. 12 cm²

Solution

Surface area = 6 × side² = 6 × (3)² = 54 cm².

Correct Answer: B — 36 cm²

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Q. What is the total surface area of a sphere with a radius of 7 cm?

A. 154 cm²
B. 196 cm²
C. 308 cm²
D. 616 cm²

Solution

Surface area of a sphere = 4πr² = 4π(7)² = 196 cm².

Correct Answer: B — 196 cm²

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Q. What is the volume of a sphere with a diameter of 10 cm?

A. 500/3 π cm³
B. 1000/3 π cm³
C. 250/3 π cm³
D. 300/3 π cm³

Solution

Volume = (4/3)πr³ = (4/3)π(5)³ = (4/3)π(125) = 500/3 π cm³.

Correct Answer: B — 1000/3 π cm³

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Visualising Solid Shapes

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