Question

Curved surface area of a cone is 251.2 cm² and radius of its base is 8 cm. Find its slant height and perpendicular height. ($\mathrm{\pi }$ = 3.14 )

Answer 1

Let the perpendicular height and slant height of the cone be h cm and l cm, respectively.

Radius of the base of cone, r = 8 cm

Curved surface area of the cone = 251.2 cm²

∴ $\mathrm{\pi }$rl = 251.2 cm²

$$\begin{gathered} \Rightarrow 3.14\times 8\times l=251.2 \\ \Rightarrow l=\frac{251.2}{25.12}=10\mathrm{cm} \end{gathered}$$
Now,

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