Question

A cone is 8.4 cm high and the radius of its base is 2.1cm. It is melted and recast into 10 smaller cones of radius 1.4cm. Find the height of the smaller cones formed.

Answer 1

In such type of problem, the volume will be constant.

When we equate the volume of both of the cone we will get the height of the smaller cone.

So, $\frac{1}{3}$$\pi$$R^2$H = $\frac{1}{3}$10$\pi$$r^2$h

$\Rightarrow$ ${2.1}^2$ $\times$ 8.4 = 10 $\times$ ${1.4}^2$ h

$\Rightarrow$ h = 1.89 cm