Surface Areas and Volumes — Practice Quiz
Karnataka Board · Class 10 · Mathematics
Try a 4-question quiz on Surface Areas and Volumes for Karnataka Board Class 10 Mathematics: tap an answer to check it and see why.
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Quick Quiz: Surface Areas and Volumes
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A cylinder has radius 7 cm and height 10 cm. What is its total surface area?
A hemisphere has radius 6 cm. What is its curved surface area?
A cone has base radius 5 cm and slant height 13 cm. What is its curved surface area?
A cube has edge length 8 cm. What is its volume?
Sample Questions
A sphere has radius 9 cm. What is its volume?
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3053.6 cm³
Step 1: Given radius r = 9 cm. Step 2: For a sphere, volume = (4/3)πr³. Step 3: Substitute values: Volume = (4/3) × (22/7) × 9³ = (4/3) × (22/7) × 729. Step 4: Calculate: Volume = (4 × 22 × 729)/(3 × 7) = 64152/21 = 3053.6 cm³. Remember to cube the radius first.
A cylinder has radius 4 cm and height 15 cm. What is its volume?
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754.3 cm³
Step 1: Given radius r = 4 cm and height h = 15 cm. Step 2: For a cylinder, volume = πr²h. Step 3: Substitute values: Volume = (22/7) × 4² × 15 = (22/7) × 16 × 15. Step 4: Calculate: Volume = (22 × 240)/7 = 5280/7 = 754.3 cm³. The volume is the area of the circular base times the height.
A cone has base radius 6 cm and height 8 cm. What is its volume?
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301.7 cm³
Step 1: Given radius r = 6 cm and height h = 8 cm. Step 2: For a cone, volume = (1/3)πr²h. Step 3: Substitute values: Volume = (1/3) × (22/7) × 6² × 8 = (1/3) × (22/7) × 36 × 8. Step 4: Calculate: Volume = (22 × 288)/(3 × 7) = 6336/21 = 301.7 cm³. Cone volume is one-third of cylinder volume with same base and height.
A toy consists of a cylinder with a hemisphere on top. Both have radius 3 cm, and the cylinder has height 10 cm. What is the total surface area?
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244.3 cm²
Step 1: Both shapes have radius r = 3 cm, cylinder height h = 10 cm. Step 2: Total surface area = CSA of hemisphere + CSA of cylinder + base area of cylinder. Step 3: Calculate each part: CSA of hemisphere = 2πr² = 2 × (22/7) × 9 = 56.6 cm²; CSA of cylinder = 2πrh = 2 × (22/7) × 3 × 10 = 188.6 cm²; Base area = πr² = (22/7) × 9 = 28.3 cm². Step 4: Add them: 56.6 + 188.6 + 28.3 = 244.3 cm². Note: The hemisphere covers one base of the cylinder.
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Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
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