SOLUTION: I have a tank in the shape of a frustum. I know the top circumference 272 inches and the bottom circumference of 216 inches. The height of the tank is 75 inches. My problem is t

Question 876926: I have a tank in the shape of a frustum. I know the top circumference 272 inches and the bottom circumference of 216 inches. The height of the tank is 75 inches. My problem is trying to solve the volume at different levels. I have a level transmitter that reads the volume as a percentage, but I need to know how the gallons change as percentage changes. So at 50% level I am assuming that the height of the volume is 37.5 inches, but I do not know the circumference at that level. Is there a way to figure this out without physically taking circumference measurements at different heights?
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
I assume you are talking about the frustum of a right circular cone, then the Volume(V) of the frustum is given by the following formula
V = (1/3)*pi*(R^2 +Rr +r^2)*h, where h is height of frustum, R is the radius of the base of the frustum, r is radius of the top of the frustum.
Now, here is what I think you need to do,
measure a length(L) on the surface of the frustum from the base to a point on the surface of the frustum, the relationship is
L^2 = (R - r)^2 + h^2, so you can calculate r for any point L and h

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