Question

A hollow sphere of internal and external diameters of $4$ cm and $10$ cm respectively, is melted into a cone of base diameter $5$ cm. Find the height of a cone so formed.

Answer 1

Here, the hollow sphere is melted to form a cone.

So, the volume of the material of the hollow sphere is used to make the cone.
Volume of hollow sphere $=$ Volume of the cone
$\frac{\pi }{6}(D^3-d^3)=\frac{1}{3}\pi r^{2}h$
$\frac{\pi }{6}({10}^3-5^3)=\frac{1}{3}\pi \times {2.5}^{2}h$
$h=\frac{125}{12.5}$
$h=10$ cm