Question

Curved surface area of a cone is $308c{m}^2$ and its slant height is $14$cm. Find the radius of the base and total surface area of the cone.

Answer 1

We know that the curved surface area of a cone with radius $r$ and slant height $l$ is $CSA=\pi rl$.

It is given that the curved surface area of the cone is $CSA=308$ cm${}^2$ andthe slant height is $l=14$ cm, therefore,

$CSA=\pi rl\Rightarrow 308=\frac{22}{7}\times r\times 14\Rightarrow 308=44r\Rightarrow r=\frac{308}{44}=7$

Thus, the radius of the cone is $7$ cm.

We also know that the total surface area of a cone with radius $r$ and slant height $l$ is $TSA=\pi r(l+r)$.

Here, the slant height of the cone is $l=14$ cm and radius is $7$ cm, therefore,

$TSA=\pi r(l+r)=\frac{22}{7}\times 7\times (14+7)=22\times 21=462$ cm${}^2$

Hence, the total surface area of a cone is $462$ cm${}^2$.