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Surface Areas and Volumes — Syllabus

Madhya Pradesh Board · Class 9 · Mathematics

What Surface Areas and Volumes covers in Madhya Pradesh Board Class 9 Mathematics: 4 topics, for the 2026-27 session.

30 questions20 flashcards4 formulas & key relations5 concepts

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Illustrates how a right-angled triangle, when rotated about one of its perpendicular sides, forms a right circular cone. Shows the progression from a flat triangle to a 3D cone.
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4 Topics · Madhya Pradesh Board Class 9 Mathematics · 2026-27

Topics in Surface Areas and Volumes

1

Surface Area of a Right Circular Cone

  • A right circular cone is formed by rotating a right-angled triangle about one of its perpendicular sides
  • The cone has three main measurements: height (h), radius (r), and slant height (l)
  • The relationship between height, radius, and slant height is: l² = r² + h² (Pythagoras theorem)
2

Surface Area of a Sphere and Hemisphere

  • A sphere is formed by rotating a circle about its diameter
  • A sphere has only one curved surface (no flat faces)
  • A hemisphere is half of a sphere with one curved surface and one flat circular base
3

Volume of a Right Circular Cone

  • Volume of cone is one-third the volume of cylinder with same base and height
  • This relationship can be demonstrated practically by filling a cone three times to fill a cylinder
  • The formula involves base area (πr²) multiplied by height and divided by 3
4

Volume of a Sphere and Hemisphere

  • Volume of sphere can be determined experimentally by water displacement method
  • The formula involves (4/3) times π times radius cubed
  • Volume of hemisphere is exactly half the volume of corresponding sphere

Key Concepts

A cone formed by rotatingCurved Surface Area = πrlA threeHalf of a sphere cut byVolume = (1/3)πr²h

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Frequently Asked Questions

What are the important topics in Surface Areas and Volumes for Madhya Pradesh Board Class 9 Mathematics?
Key topics in Surface Areas and Volumes include Surface Area of a Right Circular Cone, Surface Area of a Sphere and Hemisphere, Volume of a Right Circular Cone, Volume of a 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 30 practice questions on Surface Areas and Volumes. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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All Madhya Pradesh Board Class 9 Mathematics Syllabus

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