A hollow sphere has inner volume half the outer volume. Its $4/5\,th$ part is submerged when placed in water. The density of material is
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$\rho\left(\frac{\mathrm{V}}{2}\right) \mathrm{g}=\sigma \frac{4}{5}(\mathrm{V}) \mathrm{g}$

$\rho=\sigma\left(\frac{8}{5}\right)$

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