Chapter 10 of 12
Syllabus
Surface areas and Volumes — Syllabus
Karnataka Board · Class 9 · Mathematics
What Surface areas and Volumes covers in Karnataka Board Class 9 Mathematics: 4 topics, for the 2026-27 session.
45 questions20 flashcards3 formulas & key relations4 concepts
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4 Topics · Karnataka Board Class 9 Mathematics · 2026-27
Topics in Surface areas and Volumes
1
Surface Area of Right Circular Cone
- A right circular cone is formed by rotating a right-angled triangle about one of its perpendicular sides
- Key elements: vertex (A), height (h), radius (r), slant height (l)
- Relationship between dimensions: l² = r² + h² (Pythagoras theorem)
2
Surface Area of Sphere and Hemisphere
- Sphere is formed by rotating a circle about its diameter
- All points on sphere are equidistant from center (radius)
- Hemisphere is half of a sphere with one curved face and one flat circular base
3
Volume of Right Circular Cone
- Volume of cone is one-third of volume of cylinder with same base and height
- Experimental verification: 3 cone-fulls fill 1 cylinder completely
- Height must be perpendicular distance from vertex to base
4
Volume of Sphere and Hemisphere
- Volume formulas derived from water displacement experiments
- Sphere volume is (4/3) times the cube of radius
- Hemisphere volume is exactly half of sphere volume
Key Concepts
A cone has curved surface areaSphere surface area = 4πr²Hemisphere is half a sphereVolume = ⅓πr²h
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Start This ChapterFrequently Asked Questions
What are the important topics in Surface areas and Volumes for Karnataka Board Class 9 Mathematics?
Key topics in Surface areas and Volumes include Surface Area of Right Circular Cone, Surface Area of Sphere and Hemisphere, Volume of Right Circular Cone, Volume of Sphere and Hemisphere. Study these first, then practise questions on each for Class 9 exams.
How should I revise Surface areas and Volumes for Class 9 exams?
Learn the core ideas first, then work through the 45 practice questions on Surface areas and Volumes. Revise definitions regularly and use flashcards for quick recall before the exam.
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.
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