A metal pipe with outer radius of 10cm ,inner radius of 8cm and length of 20 have allowed errors of 1cm, 0.5cm and 2cm respectively. If need to estimate the worst-case error in volume.
So I know that volume = (pi*r1^2*l) -(pi*r2^2*l)
Then using partial differentiation I got
Vr1 = 2pi*r1*l
Vr2 = -2pi*r2*l
Vl = pi *r1^2 - pi*r2^2
V(10,8,20) = 720pi
is this the correct formula to calculate error
abs(e) = abs(Vri *E1) +abs(Vr2 *E2) +abs(Vl *E3)
Im not sure which error terms I should sub in, should i convert allowed error into a decimal or simply sub in as they are?
Any help would be great