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Density: Cube of Aluminum to Copper Sphere

  • #1

Homework Statement


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

Homework Equations


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

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.
 

Answers and Replies

  • #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!
 
  • #3
haruspex
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219.676 = 4/3pi(r3)
Radius = 52.4438 cm
Your equation cannot possibly produce a radius that large. Check the calculation.
 
  • #4
haruspex
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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!
We crossed in the post.
 

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