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.