Question

Perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone.

Answer 1

Let the radius of the base of the cone be r cm.

Height of the cone, h = 12 cm

Slant height of the cone, l = 13 cm

Now,

$$\begin{gathered} r^2+h^2=l^2 \\ \Rightarrow r^2+{\left(12\right)}^2={\left(13\right)}^2 \\ \Rightarrow r^2+144=169 \\ \Rightarrow r^2=169-144=25 \\ \Rightarrow r=\sqrt{25}=5\mathrm{cm} \end{gathered}$$
Thus, the radius of the base of the cone is 5 cm.