Question

The radius of a 12 inch right circular cylinder is measured to be 4 inches, but with a possible error of ±0.2 inch. What is the resulting possible error in the volume of the cylinder? Include units in your answer.

Answer 1

nominal ... π * 4^2 * 12

max ... π * 4.2^2 * 12

min ... π * 3.8^2 * 12

units are in^3

Answer 2

If we apply linear approximation using calculus, then:
V=πr^2h
dV/dr=2πrh
ΔV≈2πrhΔr
=2π(4)(12)(+0.2-(-0.2))
=2π(4)(12)(0.4)
=38.4π