By conservation of angular momentum: \(I_1\omega_1=I_2\omega_2\). \(I=\frac{2}{5}MR^2\). Since density is constant and volume doubles... but radius doubles: mass \(\propto R^3\), so \(M_2=8M_1\). \(I_2=\frac{2}{5}(8M_1)(2R)^2=\frac{2}{5}\times8M_1\times4R^2=\frac{64}{5}M_1R^2\). \(I_1=\frac{2}{5}M_1R^2\). \(T_2=T_1\times\frac{I_2}{I_1}=27\times32=864\)... Hmm, if only radius doubles (not mass): \(I_2=\frac{2}{5}M(2R)^2=4I_1\). \(T_2=4\times27=108\ \text{days}\).