SOLUTION: In order to double the capacity of a spherical balloon, by what percentage must the area of the material on its surface be increased?
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Question 1181743: In order to double the capacity of a spherical balloon, by what percentage must the area of the material on its surface be increased? Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! The volume of a sphere = V = 4/3pi*R^3
V1 = 4/3pi*R1^3
V2 = 4/3pi*R2^3
If the volume is doubled, V2 = 2V1 -> 4/3pi*R2^3 = 8/3pi*R1^3
Thus, R2 = (2)^(1/3)*R1
Since the surface area of a sphere = S = 4pi*R^2, S2/S1 = R2^2/R1^2 =
((2)^(1/3)*R1)^2/R1^2 = (4)^(1/3) = 1.587
Thus the surface area must increase by 58.7%
