Question

a cube made of wood and a cube made of gold have exactly the same mass. how does the volume of the cube of wood compare to the volume of the cube of gold? there is not enough information to compare the volume of the two cubes. the volume of the wood cube is greater than the volume of the gold cube. both cubes have the same volume, because they have the same mass. the volume of the gold cube is greater than the volume of the wood cube.

Explanation:

Step1: Recall density - mass - volume relationship

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume. Rearranging for volume gives $V = \frac{m}{
ho}$.

Step2: Compare densities

The density of gold is much greater than the density of wood, i.e., $
ho_{gold}>
ho_{wood}$.

Step3: Analyze volumes with same mass

Since $m_{wood}=m_{gold}$, and $V=\frac{m}{
ho}$, when $m$ is constant, the volume is inversely - proportional to the density. So, $V_{wood}>V_{gold}$.

Answer:

The volume of the wood cube is greater than the volume of the gold cube.