Firstly, \(\displaystyle{I}\propto{m}{r}^{{{2}}}\)

\(\displaystyle{m}={\frac{{{4}}}{{{3}}}}\pi{r}^{{{3}}}\rho_{{{s}{t}{e}{e}{l}}}\)

As sphere 2 has twice the radius, same destiny< its mass is greater by a factor of \(\displaystyle{2}^{{{3}}}={8}\)

The extra mass is also distributed farther from the center \(\displaystyle{\left({r}_{{2}}={2}{r}_{{1}}\right)}\), thus,

\(\displaystyle{I}\propto{m}{r}^{{{2}}}\Rightarrow{I}_{{2}}\propto{\left({8}{m}_{{1}}\right)}{\left({2}{r}_{{1}}\right)}^{{{2}}}={32}{I}_{{1}}\)

\(\displaystyle{m}={\frac{{{4}}}{{{3}}}}\pi{r}^{{{3}}}\rho_{{{s}{t}{e}{e}{l}}}\)

As sphere 2 has twice the radius, same destiny< its mass is greater by a factor of \(\displaystyle{2}^{{{3}}}={8}\)

The extra mass is also distributed farther from the center \(\displaystyle{\left({r}_{{2}}={2}{r}_{{1}}\right)}\), thus,

\(\displaystyle{I}\propto{m}{r}^{{{2}}}\Rightarrow{I}_{{2}}\propto{\left({8}{m}_{{1}}\right)}{\left({2}{r}_{{1}}\right)}^{{{2}}}={32}{I}_{{1}}\)