# Mensuration-18

### From Homeworkwiki

**A sphere of radius 8 cm is melted and recast into a right circular cone of height 32 cm. Find the radius of the base of the cone.**

**Solution:** Radius of the sphere = 8 cm

Volume of the sphere = 4/3 x π R^{3}

= 4/3 x π x 8^{3} cu. cm

Let the radius of the cone be r cm

Volume of the cone = 1/3 x π r^{2} x h

i.e. 1/3 x π x r^{2} x 32 = 32/3 π r^{2} cu. cm

According to the problem

32/3 π r^{2} = 4/3 π R^{3}

32/3 π r^{2} = 4/3 x π x 8 x 8 x 8

r^{2} = 4/3 x π x 8 x 8 x 8 x 3 / (32 x π)

= 8 x 8

r = 8

Therefore, the radius of the base of the cone = 8 cm