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.

Given :
Slant height (l) of cone = 14 cm
Curved surface area of a cone is 308 \({cm}^2\)

i) Let the radius Of the circular end of the cone be r.

We know that,

CSA of cone
= \({\pi}rl\)
= [\(\frac{22}{7} × r × 14 cm\)]
= [\(22 × 2 × r cm\)
= 44r cm

\(\Rightarrow \) 308 \({cm}^2\) = 44r cm ...(Given)
\(\Rightarrow \) r = \(\frac{308}{44} cm\) = 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
= [\({\pi}rl\) + \({\pi}{r}^2\)]
= [\(308 + \frac{22}{7} × (7)^2\) \({cm}^2\)]
= [308 + 154] \({cm}^2\)
= 462 \({cm}^2\)

Therefore, the total surface area of the cone is 462 \({cm}^2\).