a cylindrical glass tube 15.0 cm in length is filled with ethanol. the mass of the ethanol needed to fill…

Explanation:

Step1: Calculate the volume of ethanol

We know that density $\rho=\frac{m}{V}$, where $\rho$ is density, $m$ is mass and $V$ is volume. Rearranging for $V$, we get $V = \frac{m}{\rho}$. Given $m = 9.64\ g$ and $\rho=0.789\ g/mL$, so $V=\frac{9.64\ g}{0.789\ g/mL}=12.22\ mL$. Since $1\ mL = 1\ cm^{3}$, the volume $V = 12.22\ cm^{3}$.

Step2: Use the volume formula for a cylinder

The volume formula for a cylinder is $V=\pi r^{2}h$, where $h$ is the height (length) of the cylinder and $r$ is the radius. We know $V = 12.22\ cm^{3}$ and $h=15.0\ cm$. Rearranging the formula for $r^{2}$, we have $r^{2}=\frac{V}{\pi h}$. Substituting the values, $r^{2}=\frac{12.22\ cm^{3}}{\pi\times15.0\ cm}\approx0.26\ cm^{2}$. Then $r=\sqrt{0.26\ cm^{2}}\approx0.51\ cm$.

Step3: Calculate the diameter

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

Answer:

$1.02\ cm$