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Density: Cube of Aluminum to Copper Sphere

  1. Jan 13, 2016 #1
    1. The problem statement, all variables and given/known data
    What is the diameter of a copper sphere that has the same mass as a 9.00 cm× 9.00 cm× 9.00 cm cube of aluminum?

    Density of Aluminum = P(al) = 2.70g/cm3
    Density of Copper = P(cu) = 8.96 g/cm3

    Volume of Aluminum Cube = Vcube = 729 cm3

    2. Relevant equations
    Volume of a Sphere = 4/3pi(r3) - Note: We are solving for 2r (i.e. the diameter).
    Density = Mass/Volume

    3. The attempt at a solution
    1) Find the mass of the aluminum cube.
    Density = Mass/Volume - substitute in known values
    2.70g/cm3 = mass/729cm3
    Mass = 1968.3 grams

    2) Find the volume of the sphere.
    Density = Mass/Volume
    8.96 g/cm3 = 1968.3g/Volume
    Volume = 219.676 cm3

    3) Find the radius of the sphere.
    Volume of a Sphere = 4/3pi(r3) - substitute in known values
    219.676 = 4/3pi(r3)
    Radius = 52.4438 cm

    Diameter = Radius * 2 = 104.8877 cm

    Everything looks pretty spot on to me; however, my online homework says this is incorrect. Any help would be greatly appreciated.

    Thanks guys,
    Justin Daniels.

    P.S. This is my first post. Please let me know if I've failed to follow the format for posting questions, so I can correct this moving forward.
     
  2. jcsd
  3. Jan 13, 2016 #2
    Edit: I forgot to take the cubic root of the radius when solving in step 3. Sorry for the pointless thread, and thank you guys anyway!
     
  4. Jan 13, 2016 #3

    haruspex

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    Your equation cannot possibly produce a radius that large. Check the calculation.
     
  5. Jan 13, 2016 #4

    haruspex

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    We crossed in the post.
     
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