The ** volume of a sphere** is given by:

$\overline{){\mathbf{V}}{\mathbf{=}}\frac{\mathbf{4}}{\mathbf{3}}{{\mathbf{\pi r}}}^{{\mathbf{3}}}}$

**Comparing ratio of volume of nucleus to volume of atom: **

:$\frac{\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{nucleus}}{\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{atom}}=\frac{\overline{){\displaystyle \frac{\mathbf{4}}{\mathbf{3}}}\mathbf{\pi}}{\mathbf{\left(}{\mathbf{r}}_{\mathbf{nucleus}}\mathbf{\right)}}^{\mathbf{3}}}{\overline{)\frac{\mathbf{4}}{\mathbf{3}}\mathbf{\pi}}{\mathbf{\left(}{\mathbf{r}}_{\mathbf{atom}}\mathbf{\right)}}^{\mathbf{3}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\frac{\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{nucleus}}{\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{atom}}=\frac{{\mathbf{\left(}{\mathbf{r}}_{\mathbf{nucleus}}\mathbf{\right)}}^{\mathbf{3}}}{{\mathbf{\left(}{\mathbf{r}}_{\mathbf{atom}}\mathbf{\right)}}^{\mathbf{3}}}$

Carbon-12 contains 6 protons and 6 neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers).

What percentage of the carbon atoms volume is occupied by the nucleus? (Assume two significant figures.)

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