Question

If a hollow sphere of internal and external diameters 4 cm and 8 cm respectively melted into a cone of base diameter 8 cm, then find the height of the cone.

Answer 1

Volume of a sphere = \(\frac{4}{3}\)πr³ 

Volume of a right circular cone = \(\frac{1}{3}\)πr²h 

Given, 

diameter of the internal and external surfaces of a hollow spherical shell are 4 cm and 8 cm respectively. It is melted into a cone of base diameter 8 cm.

⇒ Volume of material in sphere = Volume of the cone

⇒ \(\frac{4}{3}\) x π x (4³ - 2³) =\(\frac{1}{3}\)π x 4² x h 

⇒ h = 14 cm