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

(N/A) Given: Curved surface area $= 308 \, cm^2$,Slant height $(l) = 14 \, cm$.
$(i)$ Let the radius of the base be $r \, cm$.
We know that the curved surface area of a cone is given by $\pi r l$.
$\therefore \pi r l = 308$
$\Rightarrow \frac{22}{7} \times r \times 14 = 308$
$\Rightarrow 44 \times r = 308$
$\Rightarrow r = \frac{308}{44} = 7 \, cm$.
Thus,the radius of the base is $7 \, cm$.
$(ii)$ Total surface area of a cone $= \text{Curved surface area} + \text{Base area}$.
Base area $= \pi r^2 = \frac{22}{7} \times 7^2 = 154 \, cm^2$.
Total surface area $= 308 \, cm^2 + 154 \, cm^2 = 462 \, cm^2$.