Math CentralQuandaries & Queries


Question from Tracy, a student:

I need help trying to find the volume of a 9 ft long trough that has two equilateral triangles on the end. When the water of the trough is 2 feet deep and its depth keeps increasing by 1/2 ft/minute. I have to figure out at what rate the water is flowing into the trough.
Can you point me in the right direction for finding the equation for the volume of the trough?

Hi Tracy,

The shape of the trough is a triangular prism, in fact a rectangular, triangular prism. The volume of a prism is the area of the base times the height. Thus the volume of the trough is the area of the triangular end times the length.


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