Surface Area and Volume Quiz

Grade 10 · Math · Quiz

Solve complex surface area and volume problems involving 3D shapes and composite solids.

Questions

A sphere has a surface area of 100π cm². What is its radius?
1. 5 cm
2. 10 cm
3. 25 cm
4. √10 cm
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Answer: 5 cm
4πr² = 100π → r² = 25 → r = 5 cm.
A cone has a slant height of 13 cm and a radius of 5 cm. What is its total surface area in terms of π?
1. 90π cm²
2. 65π cm²
3. 25π cm²
4. 130π cm²
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Answer: 90π cm²
SA = πrl + πr² = π(5)(13) + π(25) = 65π + 25π = 90π cm².
If the volume of a cube is 216 cm³, what is its surface area?
1. 216 cm²
2. 36 cm²
3. 72 cm²
4. 144 cm²
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Answer: 216 cm²
Side = ∛216 = 6 cm. SA = 6 × 6² = 6 × 36 = 216 cm².
A cone and a cylinder with the same base and height have equal volumes.
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Answer: False
V_cone = ⅓πr²h = ⅓ × V_cylinder. The cone's volume is one-third that of the cylinder.
A solid hemisphere has a radius of 6 cm. What is its total surface area in terms of π?
1. 108π cm²
2. 72π cm²
3. 144π cm²
4. 36π cm²
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Answer: 108π cm²
Curved surface = 2πr² = 72π. Flat base = πr² = 36π. Total = 108π cm².
A rectangular prism has dimensions 4 cm × 5 cm × 6 cm. By what factor does the volume increase if all dimensions are doubled?
1. 8
2. 2
3. 4
4. 6
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Answer: 8
Volume scales with the cube of linear dimensions: 2³ = 8.
A cylinder is melted and recast into a cone with the same radius. If the cylinder has height 9 cm, what is the height of the cone?
1. 27 cm
2. 3 cm
3. 9 cm
4. 18 cm
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Answer: 27 cm
Equal volumes: πr²(9) = ⅓πr²h_cone → h_cone = 3 × 9 = 27 cm.
The volume of a pyramid is ______ of the volume of a prism with the same base and height.
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Answer: one third
V_pyramid = ⅓ × base area × height, which is exactly one-third of the corresponding prism's volume.

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