SOLUTION: The volume of a sphere is increased by 72.8%. What is the percentage increase in the radius?

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Question 1146043: The volume of a sphere is increased by 72.8%. What is the percentage increase in the radius?
Answer by greenestamps(13200) About Me  (Show Source):
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The volume of a sphere is proportional to the cube of the radius.

An increase of 72.8% in the volume means the ratio of the new and old volumes is

%28100%2B72.8%29%2F100+=+172.8%2F100+=+1728%2F1000

The ratio of the volumes is the cube of the ratio of the radii, so the ratio of the radii is the cube root of the ratio of the volumes:

%281728%2F1000%29%5E%281%2F3%29+=+12%2F10+=+1.20

So the percent increase in the radius is 20%.