Answer: The correct answers are half percentage and 2.5 percentage.
Explanation:
The volume of the cylinder is as follows;
\(V=\pi r^{2}h\) ....... (1)
Here, r is the radius and h is the height.
On differentiating on the both side.
\(dV=2\pi rhdr\) ........ (2)
Divide (2) by (1).
\(\frac{dV}{V}=\frac{2\pi rhdr}{\pi r^{2}h}\)
\(\frac{dV}{V}=\frac{2dr}{dr}\)
\(\frac{dr}{r}=\frac{1}{2}\frac{dV}{V}\)
Put \(\frac{dV}{V}=1%\)
\(\frac{dr}{r}=\frac{1}{2}1%\)
\(\frac{dr}{r}=.005\)
\(\frac{dr}{r}=0.5%\)
To get the volume within 1% measure the radius (or the diameter) must be within half percentage of the true radius (or the diameter).
\(\frac{dr}{r}=\frac{1}{2}\frac{dV}{V}\)
Put \(\frac{dV}{V}=5%\)
\(\frac{dr}{r}=\frac{1}{2}5%\)
\(\frac{dr}{r}=0.025\)
\(\frac{dr}{r}=2.5%\)
To get the volume within 2.5% measure the radius (or the diameter) must be within half percentage of the true radius (or the diameter).
