Question

Question 3
Curved surface area of a cone is $308c{m}^2$ and its slant height is 14 cm. Find
(i) radius of the base.
(ii) total surface area of the cone. $[Assume\pi =\frac{22}{7}]$

Answer 1

(i)Given:
CSA= 308 $c{m}^2$
Slant height $l$ of the cone = 14 cm
Let the radius of the circular end of the cone be r.
We know, CSA of cone $=\pi rl$
$\left(308\right)c{m}^2=(\frac{22}{7}\times r\times 14)c{m}^2\Rightarrow r=\left(\frac{308}{44}\right)cm=7cm$
Therefore, the radius of the circular end of the cone is 7 cm.

(ii)Total surface area of cone = CSA of cone + Area of base
$=\pi rl+\pi r^2[308+\frac{22}{7}\times (7{)}^2]c{m}^2=(308+154)c{m}^2=462c{m}^2$