Expert: Paul Klarreich - 3/16/2010

Question
Paul,
How do I calcuate the volume of a ring with a triangular cross section (base =.5", Height =1") The traingular cross section sweeps out a ring of diameter 3"

Answer
Questioner: Steve
Country: United States
Category: Advanced Math
Private: No
Subject: Volume of a ring
Question: Paul,
How do I calcuate the volume of a ring with a triangular cross section (base =.5", Height =1") The traingular cross section sweeps out a ring of diameter 3"
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Try this:

1. Determine the area of the triangle.  (Obviously 1/2 bh = 1/4)

2. Locate the centroid of the triangle. (Part of the way up an altitude)

Presumably, your ring has center at (0,0), so the left corner (of the triangle) is at (1.5,0)

Now, as the triangle moves (sweeps?) about, determine the distance traveled by the centroid. (A circle whose radius you must determine, but would appear to be the x-coordinate of the centroid.)

Finally,
volume = area of triangle * distance traveled by centroid.

(This is called the THEOREM OF PAPPUS.)