Question

A hollow cylindrical pipe is of length $40cm$. Its internal and external radii are $4cm$ and $12cm$ respectively. It is melted and cast into a solid cylinder of length $20cm$. Find the radius(in cm) of the new solid.

Answer 1

We have,

$l=40cm$

$r=4cm$

$R=12cm$

We know that the volume of the hollow cylinder

$=\pi (R^2-r^2)h$

So,

$=\pi ({12}^2-4^2)\times 40$

$=\pi (144-16)\times 40$

$=\pi \left(128\right)\times 40c{m}^3$

Since, this hollow cylinder pipe is melted and cast into a solid cylinder which length is $20cm$ and let the radius be $r$

So,

$\pi r^2\times 20=\pi \left(128\right)\times 40$

$r^2=128\times 2$

$r^2=256$

$r=16cm$

Hence, this is the answer.