Question

A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone having base radius 4 cm. The height of the cone is ______.

Options

• 12 cm

• 14 cm

• 15 cm

• 18 cm

Answer 1

A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone having base radius 4 cm. The height of the cone is 14 cm.

Explanation:

Outer radius = 4 cm, inner radius = 2 cm.

Volume of the hollow sphere = `(4/3)π(4^3 - 2^3)`

= `(224/3)π cm^3`

Cone base radius = 4 cm

So cone volume = `(1/3)π(4^2)h` 

= `(16/3)πh`

Equating volumes gives `(16/3)πh = (224/3)π`

⇒ `h = 224/16` 

= 14 cm