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

External diameter of the hollow sphere = 8 cm

radius (R) = 4 cm

Internal diameter of the hollow sphere = 4 cm

radius (r) = 2 cm

Then, the volume of metal used in hollow sphere =
Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(D) - 2

Also given,

Diameter of cone = 8 cm

Therefore, radius = 4 cm

Let height of the cone = h

    \[Volume\text{ }=\text{ }1//3\text{ }\pi {{r}^{2}}h\text{ }=\text{ }1/3\text{ x }22/7\text{ x }4\text{ x }4\text{ x }h\text{ }=\text{ }352/21\text{ }h\text{ }\ldots .\text{ }\left( ii \right)\]

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(D) - 3

    \[h\text{ }=\text{ }\left( 88\text{ x }56\text{ x }21 \right)/\text{ }\left( 21\text{ x }352 \right)\text{ }=\text{ }14\text{ }cm\]

Thus, the height of the cone = 14 cm