Problem: A 10.0 cm long cylindrical glass tube, sealed at one end, is filled with ethanol. The mass of ethanol needed to fill the tube is found to be 11.88 g . The density of ethanol is 0.789 g/mL.Calculate the inner diameter of the tube in centimeters.

Calculate the volume of ethanol used:

$\mathbf{volume}\mathbf{ }\mathbf{ethanol}\mathbf{=}\mathbf{11}\mathbf{.}\mathbf{88}\mathbf{ }\cancel{\mathbf{g}}\mathbf{\times }\frac{\mathbf{1}\mathbf{ }\mathbf{mL}}{\mathbf{0}\mathbf{.}\mathbf{789}\mathbf{ }\cancel{\mathbf{g}}}$

volume ethanol = 15.057 mL

volume ethanol = volume inner space of the tube

1 mL = 1 cm³

volume of inner space = 15.057 cm³

Calculate the inner radius of the tube in centimeters:

$$\begin{gathered} \boxed{\mathbf{V}\mathbf{=}{\mathbf{\pi r}}^{\mathbf{2}}\mathbf{h}} \\ \frac{\mathbf{V}}{\mathbf{\pi h}}\mathbf{=}\frac{\cancel{\mathbf{\pi }}{\mathbf{r}}^{\mathbf{2}}\cancel{\mathbf{h}}}{\cancel{\mathbf{\pi h}}} \\ \sqrt{\frac{\mathbf{V}}{\mathbf{\pi h}}}\mathbf{=}\sqrt{{\mathbf{r}}^{\mathbf{2}}} \\ \boxed{\mathbf{r}\mathbf{=}\sqrt{\frac{\mathbf{V}}{\mathbf{\pi h}}}} \\ \mathbf{r}\mathbf{=}\sqrt{\frac{\mathbf{15}\mathbf{.}\mathbf{057}\mathbf{ }{\mathbf{cm}}^{\cancel{\mathbf{3}}\mathbf{2}}}{\mathbf{\pi }(10.0 \cancel{\mathrm{cm}})}} \\ \mathbf{r}\mathbf{=}\sqrt{\frac{\mathbf{1}\mathbf{.}\mathbf{5057}\mathbf{ }{\mathbf{cm}}^{\mathbf{2}}}{\mathbf{\pi }}} \end{gathered}$$