SOLUTION: The surface area of a sphere is directly proportional to the square of its radius r. The volume v of the sphere is directly proportional to the cube of its radius r. Find the perc

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Question 560114: The surface area of a sphere is directly proportional to the square of its radius r. The volume v of the sphere is directly proportional to the cube of its radius r. Find the percentage increase in v when s increases by 25%.
Answer by Alan3354(31487) About Me  (Show Source):
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The surface area of a sphere is directly proportional to the square of its radius r. The volume v of the sphere is directly proportional to the cube of its radius r. Find the percentage increase in v when s increases by 25%.
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A 25% increase --> 1.25 times the area
Change in radius = sqrt%281.25%29
Change in volume = %28sqrt%281.25%29%29%5E3 =~ Vol*1.3975
=~ 39.75% increase in volume