Volume and Surface Area Study Materials for Competitive Exams

Volume and Surface Area

Q. A cone has a base radius of 5 cm and a height of 12 cm. What is the total surface area of the cone?

A. 130 cm²
B. 150 cm²
C. 180 cm²
D. 200 cm²

Solution

Total Surface Area = πr(r + l), where l = √(r² + h²) = √(5² + 12²) = √169 = 13. Total Surface Area = π * 5 * (5 + 13) = 90π cm².

Correct Answer: B — 150 cm²

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Q. A cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone?

A. 12 cm³
B. 36 cm³
C. 24 cm³
D. 18 cm³

Solution

Volume = (1/3)πr²h = (1/3) * π * 3² * 4 = (1/3) * 3.14 * 9 * 4 = 37.68 cm³.

Correct Answer: C — 24 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 = side³ = 4³ = 64 cm³.

Correct Answer: B — 64 cm³

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Q. A cylinder has a height of 10 cm and a radius of 2 cm. What is the volume of the cylinder?

A. 40π cm³
B. 20π cm³
C. 30π cm³
D. 10π cm³

Solution

Volume = πr²h = π * 2² * 10 = π * 4 * 10 = 40π cm³.

Correct Answer: A — 40π cm³

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Q. A cylinder has a radius of 5 cm and a height of 7 cm. What is the total surface area of the cylinder?

A. 376.99 cm²
B. 314.16 cm²
C. 251.33 cm²
D. 157.08 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (7 + 5) = 2 * 3.14 * 5 * 12 = 376.99 cm².

Correct Answer: A — 376.99 cm²

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Q. A cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank (including the top and bottom)?

A. 56.52 m²
B. 94.25 m²
C. 113.10 m²
D. 78.54 m²

Solution

Surface Area = 2πr(h + r) = 2 * π * 3 * (5 + 3) = 2 * 3.14 * 3 * 8 = 150.72 m².

Correct Answer: B — 94.25 m²

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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 the total surface area of the box?

A. 70 cm²
B. 60 cm²
C. 100 cm²
D. 80 cm²

Solution

Surface Area = 2(lw + lh + wh) = 2(10*5 + 10*2 + 5*2) = 2(50 + 20 + 10) = 2 * 80 = 160 cm².

Correct Answer: A — 70 cm²

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

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

Solution

Volume = length * width * height = 3 * 4 * 5 = 60 cm³.

Correct Answer: A — 60 cm³

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Q. A sphere has a radius of 7 cm. What is the surface area of the sphere?

A. 154 cm²
B. 308 cm²
C. 616 cm²
D. 44 cm²

Solution

Surface Area = 4πr² = 4 * π * 7² = 4 * 3.14 * 49 = 615.44 cm².

Correct Answer: B — 308 cm²

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Q. What is the surface area of a cube with a side length of 6 cm?

A. 36 cm²
B. 72 cm²
C. 144 cm²
D. 24 cm²

Solution

Surface Area = 6 * side² = 6 * 6² = 6 * 36 = 216 cm².

Correct Answer: B — 72 cm²

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

A. 100π cm²
B. 50π cm²
C. 25π cm²
D. 75π cm²

Solution

Surface Area = 4πr² = 4π(5)² = 4π(25) = 100π cm².

Correct Answer: A — 100π cm²

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Q. What is the total surface area of a cube with a side length of 6 cm?

A. 72 cm²
B. 144 cm²
C. 36 cm²
D. 48 cm²

Solution

Surface Area = 6 * side² = 6 * 6² = 6 * 36 = 216 cm².

Correct Answer: B — 144 cm²

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Volume and Surface Area

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