# Mensuration-12

### From Homeworkwiki

**A cone is 8.4 dm high. The radius of its base is 2.1 dm. It is melted and cast into a sphere. Find the radius of the sphere.**

**Solution:** Height of the cone = 8.4 cu. dm

Radius of base = 2.1 dm

Therefore, 1/3 x π r^{2} h = 1/3 x 22/7 x 2.1 x 2.1 x 8.4 cu. dm

The cone is melted and formed into a sphere.

Therefore, Volume of the sphere = Volume of the cone

4/3 x π R^{3} = 1/3 x 22/7 x 2.1 x 2.1 x 8.4

R^{3} = 1/3 x 22/7 x 2.1 x 2.1 x 8.4 x 3/4 x 7/22

= 2.1 x 2.1 x 2.1

Hence, R of the sphere = 2.1 dm