Math CentralQuandaries & Queries


Question from I.C:

I need to find out how long a 10" round tube needs to be in order for there to be .95 cubic feet of air space


The volume of a cylindrical tube is given by $\pi \; r^2 h$ where $r$ is the radius, $h$ is the height and $\pi$ is approximately 3.1416. By '10" round tube' I assume you mean the diameter is 10" so the radius is 5 inches or $\large \frac{5}{12}$ feet. You want a volume of 0.95 cubic feet so

\[0.95 = \pi \left(\frac{5}{12}\right)^2 h\]


\[0.95 = 0.545 h.\]

Thus $h = \large \frac{0.95}{0.55} = \normalsize 1.7$ feet.


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