Question

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.

Answer 1

Surface area of sphere = 4πr² 

Curved surface area of a cone = πrl 

Given, 

surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm 

⇒ 4 × π × 5² = 5 × π × 4 × l 

⇒ l = 5 cm 

L² = h² + r² 

⇒ 5² = h² + 4² 

⇒ h² = 9 

⇒ h = 3 cm