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Johnny wants to find the volume of the paper in a fresh roll of paper towels.

Please explain what he should do to calculate the volume of the paper. Be sure to include any equipment/formulas he'll need.

The3Dude Feb 12, 2019

#1**+3 **

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

.Rom Feb 12, 2019

#2**+3 **

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.

Melody Feb 12, 2019