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| Math Central | Quandaries & Queries |
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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? |
Robert,
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.
Since triangles ABE and ACD are similar
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.
Harley
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