Final answer:
To calculate the mass of a platinum cube with a 0.04 mm edge, convert the edge length to cm, find the cube's volume, and multiply by platinum's density. The edge length in cm is 0.004 cm, volume is (0.004 cm)³, and by using the density of 21.45 g/cm³, the mass can be calculated.
Step-by-step explanation:
The student needs to calculate the mass of a cube of platinum with an edge length of 0.04 mm to answer their schoolwork question. Given that platinum crystallizes in a cubic closely packed structure, we can use the density of platinum along with the volume of the cube to find the mass. The density of platinum is typically about 21.45 g/cm³, and the cube's volume can be found by cubing the edge length. However, it's important to convert the edge length from millimeters to centimeters before calculating the volume, as standard density units are in g/cm³. The formula for calculating the volume of a cube is V = a³, where 'a' is the edge length of the cube. After finding the volume, we multiply it by the density to obtain the mass.
To demonstrate, if we convert 0.04 mm to centimeters, we get 0.004 cm (since 1 mm = 0.1 cm). Thus, the volume of the cube is V = (0.004 cm)³ = 6.4 × 10⁻¸ cm³. Finally, to find the mass, we multiply the volume by the density: mass = density × volume = 21.45 g/cm³ × 6.4 × 10⁻¸ cm³, which would provide the desired mass in grams for this platinum cube.