Surface areas and Volumes — Important Questions
Karnataka Board · Class 9 · Mathematics
45 important questions from Surface areas and Volumes for Karnataka Board Class 9 Mathematics, with answers. Includes multiple choice questions.
Interactive on Super Tutor
Studying Surface areas and Volumes? Get the full interactive chapter.
Quizzes, flashcards, AI doubt-solver and a step-by-step study plan — built for important questions and more.
Free trial, no card needed.
Important Questions from Surface areas and Volumes
Find the total surface area of a cone with base radius 5 cm and slant height 13 cm.
Show answer
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.
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.
A cone has height 12 cm and volume 1232 cm³. Find the radius of its base.
Show answer
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.
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.
+41 more questions on Surface areas and Volumes (Karnataka Board Class 9 Mathematics)
Practise AllFrequently Asked Questions
What are the important topics in Surface areas and Volumes for Karnataka Board Class 9 Mathematics?
How many important questions are there in Surface areas and Volumes?
Sources & Official References
- Karnataka SSLC — kseeb.kar.nic.in
- Dept of Pre-University Education, Karnataka
- National Education Policy 2020 — education.gov.in
Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.
More resources for Surface areas and Volumes
For serious students
Get the full Surface areas and Volumes chapter — start free.
Quizzes, flashcards, an AI doubt solver and a study plan for Karnataka Board Class 9 Mathematics. Free to start, no card needed.