A right circular cone is 3.6 cm high and 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 its height.

Explanation

Given:
For cone, `h=3.6cm`, `r=1.6cm`
Volume of the given cone`=1/3xxpir^2h=(1/3xx22/7xx1.6xx1.6xx3.6)cm^2`
Radius of the second cone`=1.2cm`.
Let its height be `h_1` then,
Volume of the second cone`=1/3xxpir^2h`
`=1/3xx22/7xx1.2xxh_1`
It is melted and recasted so, the volume of the cones would be equal,
`therefore 1/3xx22/7xx1.2xxh_1=1/3xx22/7xx1.6xx1.6xx3.6`
`h_1=(1.6xx1.6xx1.6)/(1.2xx1.2)=6.4`
Hence the height of the second cone is `6.4cm`.