Math CentralQuandaries & Queries


Question from Serena, a student:
What is the formula for finding the volume of 3-D figures


There isn't a single simple formula - sorry!

For prisms and cylinders (flat base, congruent parallel top, straight sides ) you can use base x height.

For pyramids (flat base tapering uniformly to a point) you can use 1/3 base x height.

One that works for a lot of shapes is called the "prismoidal formula", an application of "Simpson's Rule" for numerical integration.

V = 1/6 h [base area + 4(middle area) + top area]

It works for all the above, and also for spheres, ellipsoids, and paraboloids (among other shapes.) Its error is also low for many other shapes (but not all: for instance, it will grossly underestimate the volume of an hourglass!)

Good Hunting!


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