SOLUTION: The volume of a large sphere is twice the volume of a small sphere. By what factor do you need to multiply the radius of the small sphere to equal the radius of the large sphere?

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Question 1158311: The volume of a large sphere is twice the volume of a small sphere. By what factor do you need to multiply the radius of the small sphere to equal the radius of the large sphere?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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The volume of a large sphere is twice the volume of a small sphere.
By what factor do you need to multiply the radius of the small sphere to equal the radius of the large sphere?
:
a = the required factor
4%2F3pi%2A%28ar%29%5E3 = 2(4%2F3pi%2Ar%5E3)
divide both sides by 4%2F3pi
%28ar%29%5E3+=+2r%5E3
a%5E3r%5E3+=+2r%5E3
divide both sides by r^3
a^3 = 2
a = 3sqrt%282%29 (the cube root of 2)is the factor to multiply the radius to double the volume