SOLUTION: The Volume of spheres are proportional to the cubes of their radii. Two spheres of the same material weigh 3.6 kg and 2.7 kg and the radius of the smaller one is 2 cm. If the two w

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Question 101764: The Volume of spheres are proportional to the cubes of their radii. Two spheres of the same material weigh 3.6 kg and 2.7 kg and the radius of the smaller one is 2 cm. If the two were melted down and formed into a single sphere,what would be the radius..?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The mass of the sphere is equal to the density multiplied by the volume.
Since volume is proportional to the cube of the radii, then mass is also proportional to the cube of the radii.
Let’s call the mass and radius of the melted sphere, M%5B3%5D and R%5B3%5D, respectively.
What do we know.
M%5B1%5D+=+%283.6%29+kg
M%5B2%5D+=+%282.7%29+kg
R%5B2%5D+=+%282%29+cm+
Also, we know that the mass of the melted sphere will equal the sum of the two other spheres.
M%5B3%5D+=+M%5B1%5D+%2B+M%5B2%5D
We can set up a ratio since mass is proportional to the cube of the radius.
M%5B3%5D%2FM%5B2%5D+=+R%5B3%5D%5E3%2FR%5B2%5D%5E3
%28M%5B1%5D%2BM%5B2%5D%29%2FM%5B2%5D+=+R%5B3%5D%5E3%2FR%5B2%5D%5E3 Substitute for M%5B3%5D.
R%5B3%5D%5E3+=+R%5B2%5D%5E3%28M%5B1%5D%2BM%5B2%5D%29%2FM%5B2%5D Multiply both sides by R%5B2%5D%5E3.
R%5B3%5D=+2%5E3+%283.6%2B2.7%29%2F%282.7%29 Substitute with values from above.
R%5B3%5D=+%282.65%29cm