If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 c m , then the curved surface area (in cm 2 ) of this cone is :

Step-by-step solution

In △ A M C ,   A M = 3 sin 2 θ   &   M C = 3 cos 2 θ V = 1 3 π r 2 h where, r is radius and h is height of cone ⇒ V = 1 3 π 3 sin ⁡ 2 θ 2 3 + 3 cos 2 θ (since, radius of cone = A M and height of cone = M C ) ⇒ V = π 36 sin 2 ⁡ θ cos 2 ⁡ θ 2 cos 2 ⁡ θ   ∵ sin ⁡ 2 θ = 2 sin ⁡ θ cos ⁡ θ   &   cos ⁡ 2 θ = 2 cos 2 ⁡ θ - 1 = 72 &#960