Question

1.5 g/cm^3 x (48 in x 60 in x 6.0 in) x (1 kg / 1000g) x (16.387 cm^3 / 1 in^3) = 420 kg

a cylindrical glass tube 15.0 cm in length is filled with ethanol. the mass of the ethanol needed to fill the tube is found to be 9.64 g. calculate the inner diameter of the tube in cm if the density of ethanol is 0.789 g/ml.

Explanation:

Step1: Calculate the volume of ethanol

We know that density $
ho=\frac{m}{V}$, so $V = \frac{m}{
ho}$. Given $m = 9.64\ g$ and $
ho=0.789\ g/mL$. Since $1\ mL = 1\ cm^{3}$, then $V=\frac{9.64\ g}{0.789\ g/cm^{3}}=\frac{9.64}{0.789}\ cm^{3}\approx12.22\ cm^{3}$.

Step2: Use the volume - formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $h = 15.0\ cm$ is the height (length) of the cylinder and $r$ is the radius. We can re - arrange the formula to solve for $r$: $r^{2}=\frac{V}{\pi h}$. Substituting $V = 12.22\ cm^{3}$ and $h = 15.0\ cm$ into the formula, we get $r^{2}=\frac{12.22\ cm^{3}}{\pi\times15.0\ cm}$.
$r^{2}=\frac{12.22}{15.0\pi}\ cm^{2}\approx\frac{12.22}{15.0\times3.14}\ cm^{2}=\frac{12.22}{47.1}\ cm^{2}\approx0.26\ cm^{2}$. Then $r=\sqrt{0.26}\ cm\approx0.51\ cm$.

Step3: Calculate the diameter

The diameter $d = 2r$. So $d=2\times0.51\ cm = 1.02\ cm$.

Answer:

$1.02\ cm$