Calculate the volume of ethanol used:

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

**volume ethanol = 15.057 mL**

volume ethanol = volume inner space of the tube

1 mL = 1 cm^{3}

**volume of inner space = 15.057 cm ^{3}**

Calculate the inner radius of the tube in centimeters:

$\overline{)\mathbf{V}\mathbf{=}{\mathbf{\pi r}}^{\mathbf{2}}\mathbf{h}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{V}}{\mathbf{\pi h}}\mathbf{=}\frac{\overline{)\mathbf{\pi}}{\mathbf{r}}^{\mathbf{2}}\overline{)\mathbf{h}}}{\overline{)\mathbf{\pi h}}}\phantom{\rule{0ex}{0ex}}\sqrt{\frac{\mathbf{V}}{\mathbf{\pi h}}}\mathbf{=}\sqrt{{\mathbf{r}}^{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}\overline{)\mathbf{r}\mathbf{=}\sqrt{\frac{\mathbf{V}}{\mathbf{\pi h}}}}\phantom{\rule{0ex}{0ex}}\mathbf{r}\mathbf{=}\sqrt{\frac{\mathbf{15}\mathbf{.}\mathbf{057}\mathbf{}{\mathbf{cm}}^{\overline{)\mathbf{3}}\mathbf{2}}}{\mathbf{\pi}(10.0\overline{)\mathrm{cm}})}}\phantom{\rule{0ex}{0ex}}\mathbf{r}\mathbf{=}\sqrt{\frac{\mathbf{1}\mathbf{.}\mathbf{5057}\mathbf{}{\mathbf{cm}}^{\mathbf{2}}}{\mathbf{\pi}}}$

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.

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