A cube measures 1.6 cm on each edge and has a mass of 68.2 g . Calculate the density of the material that composes the cube. (The volume of a cube is equal to the edge length cubed.) \( 26.6 \mathrm{~g} / \mathrm{cm}^{3} \) \( 42.6 \mathrm{~g} / \mathrm{cm}^{3} \) \( 17 \mathrm{~g} / \mathrm{cm}^{3} \) \( 6.01 \times 10^{-2} \mathrm{~g} / \mathrm{cm}^{3} \)

To calculate the density of the material that composes the cube, we can use the formula for density: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \] 1. **Calculate the volume of the cube**: The volume \( V \) of a cube is given by the formula: \[ V = \text{edge length}^3 \] Given that the edge length of the cube is 1.6 cm: \[ V = (1.6 \, \text{cm})^3 = 1.6 \times 1.6 \times 1.6 = 4.096 \, \text{cm}^3 \] 2. **Use the mass of the cube**: The mass of the cube is given as 68.2 g. 3. **Calculate the density**: Now we can substitute the mass and volume into the density formula: \[ \text{Density} = \frac{68.2 \, \text{g}}{4.096 \, \text{cm}^3} \] Performing the division: \[ \text{Density} \approx 16.65 \, \text{g/cm}^3 \] Since this value does not match any of the provided options, let's check the calculations again for accuracy. 1. **Volume calculation**: \[ V = (1.6)^3 = 4.096 \, \text{cm}^3 \] 2. **Density calculation**: \[ \text{Density} = \frac{68.2}{4.096} \approx 16.65 \, \text{g/cm}^3 \] The closest option to our calculated density of approximately 16.65 g/cm³ is: \[ \boxed{17 \, \text{g/cm}^3} \]