Question

What will be the lateral surface area of frustum of a cone, if the area of base is 64 ∏ m ² and radius of upper one is 6m and slant height is 10m?

Answer 1

We have to determine the lateral area of frustum of a cone.

Area of base = $64\Pi m^{2}$

Since, area of circle = $\Pi R^{2}$

$\Pi R^{2} = 64\Pi$

$R^{2}=64$

$R=\pm 8$

Since, radius can'not be negative.

Therefore, the radius(R) of the base= 8 m.

Lateral area of frustum of a cone = $\Pi(R+r)l$

Lateral area of frustum of a cone = $=\Pi(8+6) \times 10$

$=\Pi(14) \times 10$

$=140\Pi$ $m^{2}$

Therefore, the lateral surface area of frustum of a cone is $140\Pi m^{2}$.