Answer:
The maximum error is approximately Ev=24%
Step-by-step explanation:
the volume of the cylinder V is
V= π/4*H*D²
where H= height and D= diameter
the variation of V will be
dV = (∂V/∂H)*dH + (∂V/∂D)*dD
dV = π/4*D²*dH +π/2*H*D*dD
if we divide by the volume V
dV /V = (π/4*D²*dH +π/2*H*D*dD )/( π/4*H*D²) = dH/H + 2*dD/D
dV /V = dH/H + 2*dD/D
then we can approximate
error in V= Ev= ΔV/V ≈ dV/V
error in H= Eh=ΔH/H ≈ dH/H
error in D= Ed=ΔD/D ≈ dD/D
thus
Ev= Eh + 2*Ed
since Ed=Eh=E=8%
Ev= Eh + 2*Ed =3*E=3*8%=24%
Ev= 24%
therefore the maximum error is approximately Ev=24%
