# Mensuration-58

### From Homeworkwiki

**A right circular cone is 3.6 cm high and the radius of its base is 1.6 cm. It is melted**

**and recast into a right circular cone with radius of its base as 1.2 cm. Find the height.**

**Solution:** For cone, h = 3.6 cm, r = 1.6 cm

Volume of the given cone = 1/3 Π r^{2} h = (1/3 x 22/7 x 1.6 x 1.6 x 3.6) cm^{3}

Radius of the second cone = 1.2 cm. Let its height be h_{1}, then

Volume of the second cone = 1/3 Π r^{2} h = 1/3 x 22/7 x 1.2 x 1.2 x h_{1}

Since the volume of the cones would be equal, so

1/3 x 22/7 x 1.2 x 1.2 x h_{1} = 1/3 x 22/7 x 1.6 x 1.6 x 3.6

=> h_{1} = (1.6 x 1.6 x 3.6) / (1.2 x 1.2) = 6.4

Hence, the height of the second cone is **6.4 cm**