# College Physics Problem 1.28

## Solution:

### Part a

The average volume is

$\displaystyle V=\pi r^2h$

$\displaystyle V=\pi \left(\frac{7.5\:cm}{2}\right)^2\left(3.25\:cm\right)$

$\displaystyle V=143.5806\:cm^3$          ☚

### Part b

Solve for the percent uncertainties of each dimension

$\displaystyle \%\:unc_r=\frac{0.002\:cm}{7.500\:cm}\times 100\%=0.027\%$

$\displaystyle \%\:unc_h=\frac{0.001\:cm}{3.25\:cm}\times 100\%=0.031\%$

The percent uncertainty in the volume is the combined effect of the uncertainties of the dimensions

$\displaystyle \%\:unc_{vol}=0.027\%+0.031\%=0.058\%$

The uncertainty in the volume is

$\displaystyle \delta _{vol}=\frac{0.058}{100}\times 143.5806=0.083\:cm^3$          ☚