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Important Questions

Surface Areas and Volumes

Gujarat Board · Class 9 · Mathematics

Most important questions from Surface Areas and Volumes for Gujarat Board Class 9 Mathematics board exam 2026. MCQs, short answer, and long answer questions with marks.

45 questions24 flashcards5 concepts

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45 Questions·
multiple choicemultiple correct

Sample Questions

1multiple correct

Which of the following statements about cones are correct?

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The slant height can be found using l² = r² + h², Total surface area = πr(l + r), Curved surface area = πrl

Correct statements: 1) l² = r² + h² (Pythagoras theorem), 2) Total surface area = πrl + πr² = πr(l + r), 3) Curved surface area = πrl. Incorrect: Volume of cone = (1/3)πr²h (not πr²h), and cone has only one circular base.

2multiple choice

If the volume of a sphere is 4851 cm³, find its radius. (Use π = 22/7)

Show answer

10.5 cm

Volume of sphere = (4/3)πr³ = 4851. So (4/3) × (22/7) × r³ = 4851. Solving: r³ = 4851 × 3 × 7 ÷ (4 × 22) = 4851 × 21 ÷ 88 = 1157.625. Therefore r³ = 1157.625, so r = 10.5 cm. Step 1: Set up equation. Step 2: Solve for r³. Step 3: Find cube root.

3multiple choice

A cone has height 12 cm and slant height 13 cm. What is its base radius?

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5 cm

Using Pythagoras theorem: l² = r² + h². So 13² = r² + 12². Therefore 169 = r² + 144. So r² = 169 - 144 = 25. Therefore r = 5 cm. Step 1: Apply Pythagoras theorem. Step 2: Substitute known values. Step 3: Solve for r.

4multiple correct

Which of the following are correct formulas for surface areas and volumes?

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Surface area of sphere = 4πr², Volume of hemisphere = (2/3)πr³, Curved surface area of hemisphere = 2πr²

Correct formulas: Surface area of sphere = 4πr², Volume of hemisphere = (2/3)πr³, Curved surface area of hemisphere = 2πr². Incorrect: Volume of cone = (1/3)πr²h (not 1/2), Total surface area of hemisphere = 3πr² (not 2πr²).

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Frequently Asked Questions

What are the important topics in Surface Areas and Volumes for Gujarat Board Class 9 Mathematics?
Surface Areas and Volumes covers several key topics that are frequently asked in Gujarat Board Class 9 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 — Gujarat Board Class 9 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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