Final answer:
To find the diameter of the copper sphere, start by determining the mass of the aluminum cube. Use that mass with the density of copper to find the volume of the copper sphere. Then, from this volume, calculate the diameter.
Step-by-step explanation:
To determine the diameter of a copper sphere with the same mass as a 17.0cm x 17.0cm x 17.0cm cube of aluminum, we must first find the mass of the aluminum cube. Knowing that the volume of a cube is obtained by cubing the length of its side (V = a³), and given that the length is 17.0cm, we find that the volume of the aluminum cube is 4913 cm³. Knowing that the density of aluminum is around 2.7 g/cm³, the mass of the aluminum cube will be about 13265 g.
Now, given that the cube and the sphere have the same mass, and that the density of copper is approximately 8.96 g/cm³, we can find the volume of the copper sphere (V = mass / density), resulting in about 1480 cm³. Knowing that the volume of a sphere is given by the formula 4/3 π·r³, we can solve for the radius (r), and thus the diameter of the sphere (being 2r).
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