Geometry question!

$\text{he'll need the radius of the roll }R\\ \text{the radius of the inner cardboard tube }r\\ \text{and the height of the roll }h\\ V = \pi h (R^2 - r^2)$

Imagine this.

You have a big solid paper cylinder.   The volume is the area of the base* height    =      $\pi*Radius^2*height$

Now you drill out the centre of it.  This is a smaller cylider, the hollow bit in the middle. 

   The volume of the the small drilled out cylinder is     also     $\pi*\color{red}{r} \color{black}adius^2*height$      I used a little r this time becaus it is a smaller radius.

Anyway I don't want the middle bit, so I throw it away.

The volume of paper is   

  $V=\pi R^2h \quad- \quad \pi\color{red}{r} \color{black}^2h\\$

This is the same as Rom's answer - his answer is just factorised.