Questions: A copper cube has a mass of 9.7 g Find the edge length of the cube. (The density of copper is 896 g / cm^3, and the volume of a cube is equal to the edge length cubed) Express your answer with the appropriate units.

Solution Steps

To find the edge length of the cube, we first need to determine its volume. The volume \( V \) of the cube can be calculated using the formula for density:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Rearranging the formula to solve for volume gives:

\[ V = \frac{\text{Mass}}{\text{Density}} \]

Substituting the given values:

\[ V = \frac{9.7 \, \text{g}}{896 \, \text{g/cm}^3} = 0.0108259 \, \text{cm}^3 \]

The volume of a cube is given by the formula:

\[ V = a^3 \]

where \( a \) is the edge length of the cube. Solving for \( a \) gives:

\[ a = \sqrt[3]{V} \]

Substituting the volume we found:

\[ a = \sqrt[3]{0.0108259 \, \text{cm}^3} \approx 0.2200 \, \text{cm} \]

Final Answer