Derive the formula for the curved surface area and total surface area of the frustum of a cone.
Consider a frustum of a cone with as height, as the slant height, ₁ and as radii of the ends where
Construction:
Extended side and of the frustum of cone to meet at
The frustum of a cone can be viewed as a difference of two right circular cones
Let h₁ and l₁ be the height and slant height of cone OAB and h₂ and l₂ be the height and slant height of cone respectively.
(Since both cones are right circular cones)
(Common)
Therefore, (AA criterion of similarity)
(Corresponding sides of similar triangles are proportional)
Subtracting 1 from both sides we get
or
Subtracting 1 from both sides we get
Therefore, CSA of the frustum of the cone
TSA of the frustum of the cone
Hence Proved.