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Important Questions

Surface Areas and Volumes

Karnataka Board · Class 10 · Mathematics

Most important questions from Surface Areas and Volumes for Karnataka Board Class 10 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

45 questions20 flashcards4 concepts

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45 Questions·
multiple choice

Sample Questions

1multiple choice
1 marks

A sphere has radius 9 cm. What is its volume?

Show answer

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.

2multiple choice
1 marks

A cylinder has radius 4 cm and height 15 cm. What is its volume?

Show answer

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.

3multiple choice
1 marks

A cone has base radius 6 cm and height 8 cm. What is its volume?

Show answer

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.

4multiple choice
1 marks

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?

Show answer

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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Frequently Asked Questions

What are the important topics in Surface Areas and Volumes for Karnataka Board Class 10 Mathematics?
Surface Areas and Volumes covers several key topics that are frequently asked in Karnataka Board Class 10 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Surface Areas and Volumes — Karnataka Board Class 10 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.
How many important questions are there in Surface Areas and Volumes?
There are 45 practice questions available for Surface Areas and Volumes. These cover multiple question types including MCQs, short answer, and long answer questions.

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