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.
Please explain in detail!

I know that V = pir^2h
r = 4 and h = 12
V = pi(4^2)(12) = 603.186

Now what do I do?

Answer 1

Given:
r = radius = 4
h = height = 12
dr = error in radius = 0.2

What we want to find
dV = error in volume

Use the derivative to find the differential dV
V = pi*r^2*h
dV/dr = d/dr[ pi*r^2*h ]
dV/dr = 2pi*r*h
dV = 2pi*r*h*dr
dV = 2pi*4*12*0.2
dV = 19.2pi

So if the error in measuring the radius is +-0.2 inches, then the error in the cylinder volume is +-19.2pi cubic inches (we either measure the volume to be 19.2pi cubic inches too big, or 19.2pi cubic inches too small)

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Final Answer: Plus or minus 19.2pi cubic inches

Note: your teacher may want you to drop the "plus or minus" part