Volume and Surface Area Study Materials for Competitive Exams

Volume and Surface Area

Q. A cone has a base radius of 4 cm and a height of 9 cm. What is the total surface area of the cone?

A. 50.24 cm²
B. 75.36 cm²
C. 100.48 cm²
D. 125.60 cm²

Solution

Total Surface Area = πr(r + l), where l = √(r² + h²) = √(4² + 9²) = √(16 + 81) = √97. Total Surface Area = π * 4 * (4 + √97).

Correct Answer: B — 75.36 cm²

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Q. A cone has a base radius of 4 cm and a slant height of 5 cm. What is the lateral surface area of the cone?

A. 40π cm²
B. 20π cm²
C. 30π cm²
D. 25π cm²

Solution

Lateral Surface Area = πrl = π * 4 * 5 = 20π cm².

Correct Answer: A — 40π cm²

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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 cone has a radius of 3 cm and a height of 4 cm. What is the volume of the cone? (Use π = 3.14)

A. 37.68 cm³
B. 12.56 cm³
C. 25.12 cm³
D. 18.84 cm³

Solution

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

Correct Answer: A — 37.68 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 cube has a volume of 27 cm³. What is the length of one side of the cube?

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

Solution

Side = ∛Volume = ∛27 = 3 cm.

Correct Answer: A — 3 cm

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

A. 40π cm²
B. 20π cm²
C. 30π cm²
D. 10π cm²

Solution

Lateral Surface Area = 2πrh = 2 * π * 2 * 10 = 40π cm².

Correct Answer: A — 40π cm²

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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 height of 10 cm and a radius of 2 cm. What is the volume of the cylinder? (Use π = 3.14)

A. 40 cm³
B. 60 cm³
C. 80 cm³
D. 100 cm³

Solution

Volume = πr²h = 3.14 * 2² * 10 = 125.6 cm³

Correct Answer: B — 60 cm³

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Q. A cylinder has a radius of 5 cm and a height of 10 cm. What is the total surface area of the cylinder?

A. 314 cm²
B. 150 cm²
C. 200 cm²
D. 250 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (10 + 5) = 2 * 3.14 * 5 * 15 = 471 cm².

Correct Answer: A — 314 cm²

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

A. 340 cm²
B. 400 cm²
C. 380 cm²
D. 420 cm²

Solution

Total Surface Area = 2πr(h + r) = 2 * π * 5 * (12 + 5) = 2 * 3.14 * 5 * 17 = 530 cm².

Correct Answer: A — 340 cm²

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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 cylindrical tank has a radius of 3 meters and a height of 5 meters. What is the surface area of the tank? (Use π = 3.14)

A. 56.52 m²
B. 94.2 m²
C. 94.5 m²
D. 47.1 m²

Solution

Surface Area = 2πr(h + r) = 2 * 3.14 * 3 * (5 + 3) = 94.2 m²

Correct Answer: B — 94.2 m²

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Q. A hemisphere has a radius of 5 cm. What is the total surface area of the hemisphere?

A. 157.08 cm²
B. 100.00 cm²
C. 78.54 cm²
D. 314.16 cm²

Solution

Total Surface Area = 3πr² = 3 * 3.14 * 5² = 3 * 3.14 * 25 = 157.08 cm².

Correct Answer: A — 157.08 cm²

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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 box has a length of 10 cm, a width of 5 cm, and a height of 2 cm. What is the volume of the box?

A. 100 cm³
B. 50 cm³
C. 20 cm³
D. 40 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 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 rectangular prism has dimensions of 3 cm, 4 cm, and 5 cm. What is the total surface area?

A. 62 cm²
B. 60 cm²
C. 70 cm²
D. 50 cm²

Solution

Surface Area = 2(lw + lh + wh) = 2(3*4 + 3*5 + 4*5) = 62 cm²

Correct Answer: A — 62 cm²

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Q. A rectangular prism has dimensions of 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 = l * w * h = 3 * 4 * 5 = 60 cm³.

Correct Answer: A — 60 cm³

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Q. A sphere has a diameter of 10 cm. What is its volume? (Use π = 3.14)

A. 523.33 cm³
B. 314 cm³
C. 157.08 cm³
D. 78.5 cm³

Solution

Volume = (4/3)πr³ = (4/3) * 3.14 * (5)³ = 523.33 cm³

Correct Answer: A — 523.33 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. A sphere has a radius of 7 cm. What is the volume of the sphere?

A. 143.67 cm³
B. 154.00 cm³
C. 200.00 cm³
D. 180.00 cm³

Solution

Volume = (4/3)πr³ = (4/3) * 3.14 * 7³ = (4/3) * 3.14 * 343 = 1436.76 cm³.

Correct Answer: A — 143.67 cm³

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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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Q. What is the total surface area of a sphere with a radius of 7 cm? (Use π = 3.14)

A. 615.44 cm²
B. 153.86 cm²
C. 308 cm²
D. 154 cm²

Solution

Surface Area = 4πr² = 4 * 3.14 * 7² = 615.44 cm²

Correct Answer: A — 615.44 cm²

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Volume and Surface Area

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