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Surface areas and Volumes

Karnataka Board · Class 9 · Mathematics

Most important questions from Surface areas and Volumes for Karnataka Board Class 9 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

Find the total surface area of a cone with base radius 5 cm and slant height 13 cm.

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282.9 cm²

Step 1: Given r = 5 cm, l = 13 cm. Step 2: Total surface area = curved surface area + base area = πrl + πr². Step 3: Factor out π and r to get πr(l + r). Step 4: Substitute = (22/7) × 5 × (13 + 5) = (22/7) × 5 × 18 = 1980/7 = 282.9 cm². Total surface area includes both curved surface and circular base.

2multiple choice
1 marks

The volume of a sphere is 4851 cm³. Find its radius. (Use π = 22/7)

Show answer

10.5 cm

Step 1: Given volume = 4851 cm³. Step 2: Apply volume formula (4/3)πr³ = 4851. Step 3: Substitute π = 22/7: (4/3) × (22/7) × r³ = 4851. Step 4: Solve for r³: r³ = (4851 × 3 × 7)/(4 × 22) = 101871/88 = 1157.625. Step 5: Take cube root: r = 10.5 cm. Working backwards from volume to radius requires solving the cubic equation.

3multiple choice
1 marks

A cone has height 12 cm and volume 1232 cm³. Find the radius of its base.

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7 cm

Step 1: Given h = 12 cm, V = 1232 cm³. Step 2: Apply volume formula (1/3)πr²h = 1232. Step 3: Substitute known values: (1/3) × (22/7) × r² × 12 = 1232. Step 4: Solve for r²: r² = (1232 × 3 × 7)/(22 × 12) = 25872/264 = 49. Step 5: Therefore r = 7 cm. This is a reverse application of the volume formula.

4multiple choice
1 marks

Find the volume of a hemisphere with diameter 21 cm.

Show answer

2425.5 cm³

Step 1: Given diameter = 21 cm, so radius r = 10.5 cm. Step 2: Volume of hemisphere = (2/3)πr³. Step 3: Substitute values = (2/3) × (22/7) × (10.5)³. Step 4: Calculate = (2/3) × (22/7) × 1157.625 = (2 × 22 × 1157.625)/(3 × 7) = 2425.5 cm³. Remember hemisphere volume is half of sphere volume.

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Frequently Asked Questions

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