The surface area of a sphere of radius 5cm is five times the area of the curved surface of a cone of radius 4cm. Find the height and volume of the cone (pi = 22/7)
Let R be the radius of the sphere.
Suppose the radius of cone be r and h respectively.
Surface area of the sphere = 4πR2 = 4π (5 cm)2 = 100π cm2
Curved surface area of cone = πrl = π × 4 cm × l = 4πl
Given, Surface area of the sphere = 5 × Curved surface area of the cone
∴ 100π cm2 = 5 × 4π l cm
⇒ 100π cm2 = 20πl cm
⇒ l = 5 cm
Slant height of the cone, 
∴ (4 cm)2 + h 2 = (5 cm)2
⇒ h 2 = 25 cm2 – 16 cm2
⇒ h 2 = 9 cm2
⇒ h = 3 cm
Height of the cone, h = 3 cm
∴ Volume of the cone 
