Question

Curved surface area of a cone is $308{cm}^2$ and its slant height is $14cm.$

$\left(i\right)$ Find radius of the base and

$\left(ii\right)$ total surface area of the cone.

Answer 1

Given,

Curved Surface Area of cone, $CSA=308c{m}^2$

& slant height, $l=14cm$.

$\left(i\right)$ Lets evaluate radius using curved surface area of cone formula,

$\begin{array}{cc}CSA& =\pi rl\\ \Rightarrow 308& =\frac{22}{7}\times r\times 14\\ \Rightarrow 308& =22\times r\times 2\\ \Rightarrow r& =\frac{308}{44}\\ \Rightarrow r& =7cm\end{array}$

Hence, the radius of the cone is equal to $7cm.$

$\left(ii\right)$ Lets evaluate the total surface area of the cone using curved surface area and base area,

$\begin{array}{cc}\text{Total surface area of the cone}& =\pi rl+\pi r^2\\ & =308+\frac{22}{7}\times 7\times 7\\ & =308+22\times 1\times 7\\ & =308+154\\ & =462c{m}^2\end{array}$
Hence, the total surface area of the cone is $462c{m}^2$.