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Chapter Summary

Mensuration — Chapter Summary

ICSE · Class 10 · Mathematics

Summary of Mensuration for ICSE Class 10 Mathematics. Key concepts: A cylinder is formed when, A hollow cylinder has and A cone is formed by revolving.

35 questions28 flashcards8 formulas & key relations5 concepts

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A labeled diagram showing a right circular cylinder with its height (h) and radius (r) clearly marked. An adjacent diagram shows the cylinder 'unfolded' into a rectangle (representing the curved surfa
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Overview

Mensuration deals with the measurement of surface area and volume of solids. The main solids covered are the right circular cylinder, right circular cone, sphere, hemisphere, spherical shell, hemispherical shell, hollow cylinder, and capsule. Combination solids are also included, while frustum probl

Key Concepts

A cylinder is formed when

A cylinder is formed when a rectangle is revolved about one of its sides as axis. The side about which it revolves is the height, and the generating l

A hollow cylinder has an external

A hollow cylinder has an external radius R, an internal radius r, and height h. The volume of material is \pi h(R^{2}-r^{2}), curved surface is 2 \pi

A cone is formed by revolving

A cone is formed by revolving a right-angled triangle about one of the sides containing the right angle. The radius of the base is r, the height is h,

A sphere is formed when

A sphere is formed when a circle is revolved about its diameter. It is also defined as a solid bounded by a closed surface with all points at constant

A hemisphere is half of

A hemisphere is half of a sphere, formed when a plane through the centre divides the sphere into two equal parts. Its volume is \frac{2}{3} \pi r^{3}.

Learning Objectives

  • Find curved surface area, total surface area, and volume of a cylinder, cone, sphere, hemisphere, spherical shell, hemispherical shell, and hollow cylinder.
  • Use the standard formulas for three-dimensional solids correctly in numerical problems.
  • Understand how combination solids such as capsule, tent, and dome are formed.
  • Solve application problems involving inner volume, outer volume, cost, and melting and recasting.
  • Avoid common errors in using surface area and volume formulas.

Frequently Asked Questions

What are the important topics in Mensuration for ICSE Class 10 Mathematics?
Key topics in Mensuration include Cylinder and Hollow Cylinder, Cone, Sphere, Hemisphere and Shells, Combination of Solids and Application Problems. Study these first, then practise questions on each for the ICSE Class 10 board exam.
How should I revise Mensuration for the ICSE Class 10 board exam?
Learn the core ideas first, then work through the 35 practice questions on Mensuration. 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.

More resources for Mensuration

All ICSE Class 10 Mathematics Chapter Summary

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