You\'re designing a system for a cylindrical tank that you think is about 3-feet

Question

You're designing a system for a cylindrical tank that you think is about 3-feet-high (thats the diameter, D) and a 6-feet long (thats the length, L). Your estimate is based on a cheap yardstick with inches. Thus, we assume that the uncertainty for the length of your two measured dimensions is 0.5 inches. The formula for volume of a cylinder with a diameter instead of radius is V(D,L)= ((pi)(D)^2(L))/4.

Calculate the PROPAGATED ERROR OF THE RESULTING ERROR IN THE TANK'S VOLUME. Keep units in inches for simplicity. For standards use pi=3.1416. Show detailed Calculus work.

Explanation / Answer

D= 3 feet = 36 inches

L= 6 feet = 72 inches

Volume V= pi D2*L/4=3.1416*362*72/4=73287.2448

But because of wrong measurement

D=35.5 inches L= 71.5 inches

V' = 3.1416*35.52*71.5/4=70770.7250

error = 73287.2448-70770.7250=2516.52 inces3

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