Question

A hollow sphere of internal and external diameters 4 and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.

Answer 1

Internal radius of hemisphere  `r_1 = 4/2`= 2 cm

External radius of hemisphere  `r_2 = 8/2`= 4 cm

Volume of hollow sphere `= 4/3 pi (r_2^3 - r_1^3)`

` = 4/3 pi (64 - 8)`

`= 4/3 pi xx 56`

`= (224)/3 pi cm^2`

Since,

The hemisphere melted into a cone of radius r = 4 cm

Let h be height of the cone.

Clearly, the volume of cone = volume of hemisphere

`1/3pi(4)^2 xx h = (224)/3 pi`

                   `h = (224)/6`

                   `h = 14`

Thus, the height is 14 cm.