Math CentralQuandaries & Queries


Question from robert:

12.5"@ base x 7" @ top and 40' height. How would I find the volume in cubic feet for a telephone pole with these dimensions?


I am going to assume that the 12.5" and 7" are diameters.

The pole is a truncated cone, a cone with the top cut off. If you extend the pole until it comes to a point and forms a cone then you can determine its volume by calculating the volume of the extended pole and then subtracting the volume cut off.

In my diagram I extended the pole to the point A and I let h feet be the height of the extension.

telephone pole

Since triangles ABE and ACD are similar

7 is to h as 12.5 is to 40 + h

Solve this equation for h.

Use the fact that the volume of a cone is

1/3 π r2 h

to find the volume of the cone of height 40 + h feet and subtract the volume of the cone of height h feet.


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