Math CentralQuandaries & Queries


Question from Cliff:

How long does a pipe with a 24" circumference need to be to hold 2 cubic feet?

Hi Cliff,

The circumference of a circle of radius r inches is 2 π r inches. Thus in your case

2 π r = 24 inches


r = 12/π inches.

The volume of a cylinder of radius r inches and height h inches (your pipe, standing on end) is

π r2 h square inches.

Each cubic foot is 12 by 12 by 12 inches so a cubic foot is 123 cubic inches. Thus for your pipe


π r2 h = 2 × 123 cubic inches.

But you know that r = 12/π inches so

π (12/π)2 h = 2 × 123.

Solving for h gives h = 24 π inches.

I hope this helps,

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