Question

Surface area of a cone is 188.4 sq.cm and its slant height is 10 cm. Find its perpendicular height ( $\mathrm{\pi }$= 3.14)

Answer 1

Let the radius of the base and perpendicular height of the cone be r cm and h cm, respectively.

Slant height of the cone, l = 10 cm

Surface area of the cone = 188.4 cm²

∴ $\mathrm{\pi }$rl = 188.4 cm²

$$\begin{gathered} \Rightarrow 3.14\times r\times 10=188.4 \\ \Rightarrow r=\frac{188.4}{3.14\times 10}=6\mathrm{cm} \end{gathered}$$
Now,

$$\begin{gathered} r^2+h^2=l^2 \\ \Rightarrow {\left(6\right)}^2+h^2={\left(10\right)}^2 \\ \Rightarrow 36+h^2=100 \\ \Rightarrow h^2=100-36=64 \\ \Rightarrow h=\sqrt{64}=8\mathrm{cm} \end{gathered}$$
Thus, the perpendicular height of the cone is 8 cm.