## Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

$\rho = \frac{M}{V}$ That is: $density = \frac{mass}{volume}$ (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. $\rho' = \frac{M}{8V} = \frac{\rho}{8}$