Math CentralQuandaries & Queries


Subject: Integration
Name: Sam
Who are you: Student

Find the volume of a frustum of a pyramid with square base of side b, square top of side a, and height h.
Thanks for the help.

Hi Sam,

Imagine that you move up from the base x units and cut a horizontal slice through the pyramid as in the diagram.


Suppose that the slice is of thickness deltax. The top of the slice is a square and let f(x) be the length of a side of the square. Hence the volume of the slice is approximately

f(x)2 deltax square units.

From integration theory you can now conclude that the volume of the frustum is


All that remains is to find f(x). That you can accomplish using similar triangles.


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