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# Curved surface area of a cone is 308 $${cm}^2$$ and its slant height is 14 cm. Find i) radius of the base andii) 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 $${cm}^2$$.