Questions: Due date 9/30/24 3:35 PM PDF w/o expl 9. Cube Density 0210 pts possible The mass of a solid cube is 1230 g, and each edge has a length of 5.69 cm. Find the density of the cube. Answer in units of kg / m^3.

Solution Steps

The volume \( V \) of a cube is given by the formula: \[ V = \text{side length}^3 \] Given that each edge of the cube is 5.69 cm, we convert this to meters: \[ 5.69 \, \text{cm} = 0.0569 \, \text{m} \] Now, calculate the volume: \[ V = (0.0569 \, \text{m})^3 = 0.0001843 \, \text{m}^3 \]

The mass of the cube is given as 1230 g. Convert this to kilograms: \[ 1230 \, \text{g} = 1.230 \, \text{kg} \]

Density \( \rho \) is defined as mass per unit volume: \[ \rho = \frac{\text{mass}}{\text{volume}} = \frac{1.230 \, \text{kg}}{0.0001843 \, \text{m}^3} \] Calculate the density: \[ \rho = 6674.5 \, \text{kg/m}^3 \]

Final Answer