Question

The radius of a cone is $5cm$ and vertical height is $12cm$. Find the area of the curved surface.

Answer 1

Step 1: Find the slant height of the cone.

Let the slant height of the cone be $lcm$

Given that, the radius $r$ of the cone is $5cm$ and the vertical height of the cone is $12cm$

According to the Pythagoras theorem, $l^2=h^2+r^2$

$$\begin{gathered} \Rightarrow l^2={\left(12\right)}^2+{\left(5\right)}^2 \\ \Rightarrow l^2=144+25 \\ \Rightarrow l^2=169 \\ \Rightarrow l=13cm \end{gathered}$$

Step 2: Find the curved surface area of the cone.

The curved surface area of the cone of radius $r$ and slant height $l$ $=\mathrm{\pi rl}$

$$\begin{gathered} =\frac{22}{7}\times 5\times 13\left(\pi =\frac{22}{7}\right) \\ =204.28c{m}^2 \end{gathered}$$

Therefore, the curved surface area of the cone is $204.28c{m}^2$