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