# Curved surface area of a cone is $308 \mathrm{~cm}^{2}$ and its slant height is $14 \mathrm{~cm}$. Find(i) radius of the base and (ii) total surface area of the cone.

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Given:

The curved surface area of a cone is $308\ cm^2$ and its slant height is $14\ cm$.

To do:

We have to find the radius of the base and the total surface area of the cone.

Solution:

The curved surface area of the cone $= 308\ cm^2$

Slant height of the cone $(l) = 14\ cm$

This implies,

Radius of the base of the cone $(r)=\frac{\text { Curved surface }}{2 \pi h}$

$=\frac{308 \times 7}{22 \times 14}$

$=7 \mathrm{~cm}$

The total surface area of the cone $=\pi r l+\pi r^{2}$

$=308+\frac{22}{7} \times 7 \times 7$

$=308+154$

$=462 \mathrm{~cm}^{2}$

Hence, the radius of the base and the total surface area of the cone are $7 \mathrm{~cm}$ and $462 \mathrm{~cm}^{2}$ respectively.

Updated on 10-Oct-2022 13:46:36