Relation Among Radius, Height
and Slant Height

A O B C h l r

Consider a cone with vertex A. Let OB = r cm be the radius of the base of the cone.

Join A to O (the centre of the base). Then, AO is the height of the cone, i.e., AO = h.

AC and AB are the slant heights of the cone, i.e., AC = AB = l.

In right triangle AOB, by Pythagoras Theorem:

→ AB2 = AO2 + OB2
→ l2 = h2 + r2
→ l = h2 + r2
The slant height is equal to the square root of the sum of squares of height h and radius of circular base i.e
h2 + r2 .