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.
Surface area of sphere = 4πr2
Curved syrface 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