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 = 4πr^{2}

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 × 5^{2} = 5 × π × 4 × l

⇒ l = 5 cm

L^{2} = h^{2} + r^{2}

⇒ 5^{2} = h^{2} + 4^{2}

⇒ h^{2} = 9

⇒ h = 3 cm

9