Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find

(i) radius of the base and

(ii) total surface area of the cone.

(i) Let the radius be r cm.

Given,

Curved surface area of cone = 308 cm²

$\Rightarrow πrl = 308 \\[1em] \Rightarrow r = \dfrac{308}{πl} \\[1em] \Rightarrow r = \dfrac{308}{\dfrac{22}{7} \times 14} \\[1em] \Rightarrow r = \dfrac{308}{22 \times 2} \\[1em] \Rightarrow r = \dfrac{308}{44} \\[1em] \Rightarrow r = 7 \text{ cm}$

Hence, radius of the base of cone = 7 cm.

(ii) By formula,

Total surface area of cone (T.S.A.) = πr(l + r)

Substituting values we get :

T.S.A. = $\dfrac{22}{7}$ × 7 × (7 + 14)

= $\dfrac{22}{7}$ × 7 x 21

= 22 × 21

= 462 cm².

Hence, the total surface area of the cone is 462 cm².