The lateral surface area of frustum of a right circular cone if the area of its base is 16π cm² and the diameter of circular upper surface is 4 cm and slant height 6 cm, will be

Solution (By Examveda Team)

Base Area = 16π
πR² = 16π
R = 4
Given r = 2
∵ ΔABC ≅ ΔADE
$$\eqalign{ & \therefore \frac{{{\text{BC}}}}{{{\text{DE}}}} = \frac{{{\text{AC}}}}{{{\text{AE}}}} \cr & \frac{4}{8} = \frac{6}{{{\text{AE}}}} \cr & {\text{AE}} = 12 = {\text{L}} \cr} $$
Surface Area of frustum
= πRL - πr$$l$$
= π × 4 × 12 - π × 2 × 6
= 48π - 12π
= 36π