Math CentralQuandaries & Queries


Question from Andrew, a student:

Find the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in., whose upper base is a square with a side 3in., and whose altitude is 12 in. Round your answer to the nearest whole number.

A. 47cu in. C. 226 cu in.
B. 196 cu in. D. 1036 cu in.


The volume of a pyramid is (1/3)Ah, where A is the area of the base and h is the height.

A frustum is just the lower part (i.e. not including the tip). So the volume of the frustum is the same as the volume of the full-size pyramid MINUS the volume of the "missing" pyramid on top.

So you need to find out how tall the pyramid would be if it weren't chopped off.

You can see that half the lengths of the sides are 2.5 inches and 1.5 inches. It takes 12 inches of vertical space to go from 2.5 to 1.5, so how many inches of vertical space does it take to go from 2.5 all the way to 0 (the point of the pyramid)?

Knowing this, you can calculate the two pyramid volumes, subtract and get one of the answers in the list.

Stephen La Rocque.

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