Final answer:
To calculate the side length of the interior cubical cavity, subtract the volume of 36.3 kg of aluminum from the volume of the entire cube and then take the cube root of the resulting volume. The side length is approximately 0.0701 m.
Step-by-step explanation:
To determine the length of each side of the interior cubical cavity within a cast aluminum object, we must use the density of aluminum and the given mass of the object. Since the density of aluminum is 2700 kg/m³ (2.70 g/cm³), we can calculate the volume of aluminum that would have a mass of 36.3 kg, then subtract this volume from the volume of the entire cubical object to find the volume of the cavity.
First, calculate the volume of 36.3 kg of aluminum using the density:
- Volume of aluminum = Mass / Density = 36.3 kg / 2700 kg/m³ = 0.01348148 m³
Next, calculate the volume of the entire cube:
- Volume of the cube = Side³ = (0.240 m)³ = 0.013824 m³
Now, subtract the volume of aluminum from the total volume to find the volume of the cavity:
- Volume of cavity = Total volume - Volume of aluminum = 0.013824 m³ - 0.01348148 m³ = 0.00034252 m³
Finally, find the side length of the cavity by taking the cube root of the cavity volume:
- Side length of cavity = ³√(Volume of cavity) = ³√(0.00034252 m³) ≈ 0.0701 m