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

(i) radius of the base

(ii) total surface area of the cone.

(i) Given, Curved surface area of a cone = 308 cm² and slant height = 14 cm.

We know that,

Curved surface area of cone = πrl.

∴ πrl = 308

⇒ $\dfrac{22}{7}$ x r x 14 = 308

⇒ 22 × r × 2 = 308

⇒ 44r = 308

⇒ r = $\dfrac{308}{44}$ = 7 cm.

Hence, the radius of the base = 7 cm.

(ii) Total surface area of cone = πr(l + r)

Putting values in above equation we get,

Total surface area = $\dfrac{22}{7}$ x 7 x (14 + 7) = 22 × 1 × 21 = 462 cm².

Hence, the total surface area of right circular cone = 462 cm².