Question

Curved surface area of a cone is $308$ ${\text{cm}}^2$ and its slant height is $14$ cm, then find total surface area of the cone.

Answer 1

if curved surface area of a cone $\pi rl=308c{m}^2$
height $h=l=14cm$

$r=?$
CSA of a cone $=\pi rl$
$308=\frac{22}{7}\times r\times 14$
$308=44\times r$
$\therefore r=\frac{308}{44}$
$\therefore r=7cm$
Then $T.S.A=?$
TSA of a cone = $\pi r(r+l)$
$=\frac{22}{7}\times 7(7+14)$
$=\frac{22}{7}\times 7\times 21$
$=22\times 21$
$=462c{m}^2$