Answer
(a) The density does not change.
(b) The density decreases by a factor of 8.
Work Step by Step
$density = \frac{mass}{volume}$
$\rho = \frac{M}{V}$
(a) Density depends on the material. If the type of material does not change, then the density does not change. If the volume increases by a factor of 8, then the mass will also increase by a factor of 8 since the material is the same. Therefore, the density does not change.
$\rho^* = \frac{8M}{8V} = \frac{M}{V} = \rho$
(b) If each of the object's three dimensions is increased by a factor of 2, then the volume increases by a factor of 8. Since the mass does not change, then the density decreases by a factor of 8.
$\rho' = \frac{M}{8V} = \frac{\rho}{8}$
