Math CentralQuandaries & Queries


Question from Ken, a parent:

I have a roll that is 13.5 inches wide ( OD) , and is wound on a 3 inch core. the thickness of the material is 3.5 thick.
Do you know of a formula that can calculate the linear feet on that roll??

Hi Ken,

The formula you want is in Penny's response to an earlier question. Look at it to see if this what you want. If I am correct then using the notation in her response you have $R = 13.5$ inches, $r = 3$ inches and $t = 3.5$ inches. Thus if $T$ is the length of the material on the roll then

\[L = \frac{\pi \; \left(R^2 - r^2\right)}{t} \]


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