Maths Chapter 12: Surface Areas and Volumes

In this chapter, you will study how to determine the surface area of an object formed by combining any two of the basic solids - cuboid, cone, cylinder, sphere and hemisphere.

Also, how to find the volume of objects formed by combining any two of a cuboid, cone, cylinder, sphere and hemisphere.

Given a right circular cone, which is sliced through by a plane parallel to its base, when the smaller conical portion is removed, the resulting solid is called a Frustum of a Right Circular Cone. The formulae involving the frustum of a cone are:

Volume of a frustum of a cone = 1/3 × πh × (r₁² + r₂² + r₁r₂)

Curved surface area of a frustum of a cone = πl(r₁ + r₂)

Total surface area of frustum of a cone = πl(r₁ + r₂) + π(r₁² + r₂²)