📘 Class 10 · Mathematics

Chapter 10: Mensuration

5 lessons

Mensuration extends Class 9's surface area and volume formulas to combined solids — a cone sitting on a hemisphere, a cylinder with a cone removed — and to problems where one solid is reshaped or melted into another.

1
Introduction to Mensuration
Formulae for surface areas and volumes of 3D objects.
 2
Exercise 10.1 — Surface Areas and Volumes
Problems based on surface areas and volumes.
 3
Exercise 10.2 — Surface Area of Combined Solids
Surface areas of combination of solids.
 4
Exercise 10.3 — Volume of Combined Solids
Volumes of combination of solids.
 5
Exercise 10.4 — Conversion of Solids
Conversion of solids from one shape to another.

The hidden-surface trap

Including a shared, internal surface — like the circle where a cone meets a hemisphere — in a combined solid's total surface area is the single most common mistake; that surface is hidden, not exposed, and has to be excluded, so only the cone's curved surface and the hemisphere's curved surface actually count. In conversion-of-solids problems, it's volume that stays constant, not surface area, which is easy to forget under pressure.