Question

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

Answer 1

Given :

Curved surface area of the cone $=308c{m}^2$ and Slant height or $l=14$ cm.

Curved surface area of the cone $=\pi rl$

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

$r=\frac{(308\times 7)}{(22\times 14)}$

$r=7cm$

Total surface area of the cone $=\pi r(r+l)$

$=(\frac{22}{7}\times 7)(7+14)$

$=22\times 21$

Total surface area of the cone $=462c{m}^2$

So, the radius of the base of the cone is $7$ cm and the total surface area of the cone is $462c{m}^2$.