v = πr^2h
dv = 2πrh dr + πr^2 dh
h is assumed exact, so dh=0.
dv = 2πrh dr
dr = 0.2, so
dv = 2π(4)(12)(.2) = 19.2π
and that's ±
Your estimate assumes that the height was also measured with an error. The problem does not say that. If that is stipulated, then your answer is correct.
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.
r = 4 in.
h = 12 in.
V = pi*r^2 * h = 3.14*4^2 * 12 = 602.88
m^3.
r = 4.2 in.
h = 12.2 in.
V = 3.14*4.2^2 * 12.2 = 675.75 in^3
Is this right? If not can you please give me the solution? I spent a while on this.
1 answer
3 answers