Question

How many spheres of diameter $12cm$ each, can be made from a metallic cylinder of diameter $8cm$? The height of cylinder is $90cm$.

Answer 1

Let us assume that n spheres can be made

Cylinder $D=8cm$ and $h=90cm$

$r=4cm$

volume of cylinder $V=\pi r^{2}h$

$V=\pi \times 4\times 4\times 90=1440\pi$

As $D=12$cm so $r=6cm$

Now volume of one sphere

$V^{{}^{\prime }}=\frac{4}{3}\pi r^3=\frac{4}{3}\times \pi \times 6\times 6\times 6=288\pi$

As there are $n$ spheres

$n\times 288\pi =1440\pi$

$n=5$

There can be five sphere can be made from cylinder.