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.

V = πr²h = 16πr²
dV/dr = 32πr
dV = 16πr dr
Let dV and dr represent the change (or error) in volume and radius. In this case, dr = ±0.1 inch, r = 4 inches, and we are asked for dV, the resulting possible error in the cylinder's volume.
dV = 16πr dr
dV = 16π(4) ±0.2
dV = ±40.2 inches³ ---> MY ANSWER

Answer 1

Hmmm. h is constant at 12, so

V = πr^2h = 12πr^2
dV = 24πr dr
...

Answer 2

is this the correct method though?

Answer 3

my answer would then be 30.16