# Mensuration-20

### From Homeworkwiki

**A solid cone is 27 cm high and the radius of its base is 6 cm. Three such cones are melted and recast into a solid sphere.**

**Determine the diameter of the sphere.**

**Solution:** For solid cone, r = 6 cm, h = 27 cm

Volume of the cone = 1/3 π r^{2} h = 1/3 x 22/7 x 6 x 6 x 27 cu. cm

Volume of 3 cones = 3 x 1/3 x 22/7 x 6 x 6 x 27 cu. cm

If the radius of the sphere is R then volume of the sphere

= 4/3 π R^{3} = 22/7 x 6 x 6 x 27

R^{3} = 22/7 x 6 x 6 x 27 x 7/22 x 3/4 = 9 x 9 x 9

Therefore, R = 9 cm.

Diameter = 2 R = 18 cm