Show that $\frac{21}{r}$ spheres can be made by melting a metal cylinder of radius r & altitude 2.24m

Question

A solid cylinder of radius r and of altitude 2.24m is heated with any metal wastage & spheres of radius 2r are made. Show that $\frac{21}{r}$ spheres can be made.

I'm really stuck here & even don't know where should I begin, Your hints would be highly appreciated

Many Thanks :)

Answer 1

First shall we calculate the total volume of the cylinder using $\pi r ^2 h$

Substituting

$2.24 \pi r ^2 $

Next the volume of a one sphere $\frac{4}{3} \pi r^3$

$\frac{24}{3} \pi r^3$

Now you can divide