tion 18 of 20
One component of a metal sculpture consists of a solid cube with an edge of length $33.7 \mathrm{~cm}$. The alloy used to make the cube has a density of $7130 \mathrm{~kg} / \mathrm{m}^{3}$. Find the cube's mass.
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Step 1 ：The mass of an object is given by the formula: \(m = \rho \times V\), where \(m\) is the mass, \(\rho\) is the density, and \(V\) is the volume.

Step 2 ：The volume of a cube is given by the formula: \(V = a^3\), where \(a\) is the length of the edge of the cube.

Step 3 ：We need to calculate the volume of the cube first, then multiply it by the density to get the mass.

Step 4 ：However, we need to be careful with the units. The edge length is given in cm, but the density is given in kg/m^3. So, we need to convert the edge length from cm to m before calculating the volume.

Step 5 ：Given edge length in cm is 33.7, so in meters it is 0.337.

Step 6 ：Calculate the volume of the cube: \(V = (0.337)^3 = 0.0383 \, m^3\).

Step 7 ：Given density is 7130 kg/m^3, calculate the mass: \(m = \rho \times V = 7130 \times 0.0383 = 272.88 \, kg\).

Step 8 ：\(\boxed{272.88 \, \text{kg}}\) is the mass of the cube.