Question:
Curved surface area of a cone is $308 \mathrm{~cm}^{2}$ and its slant height is $14 \mathrm{~cm}$. Find the radius of the base and total surface area of the cone.
Solution:
(1) It is given that
Slant height of cone = 14 cm
Let radius of circular end of cone = r
Curved surface area of cone = πrl
$\Rightarrow 308 \mathrm{~cm}^{2}=22 / 7 * \mathrm{r} * 14$
⟹ r = 308/44 = 7 cm
Thus radius of circular end of cone = 7 cm.
(ii) It is given that C.S.A $=308 \mathrm{~cm}^{2}$
We know that total surface area of a cone
= curved surface area of a cone + Area of base
$=\pi r l+\pi r^{2}$
$=\left[308+\left(22 / 7 * 7^{2}\right)\right]$
= 308 + 154
$=462 \mathrm{~cm}^{2}$
Thus total surface area of the cone is $462 \mathrm{~cm}^{2}$