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Bunuel
A clown blows up a spherical balloon such that its volume increases at a constant rate. It takes 3 seconds for the radius of the balloon to increase from 1 inch to 2 inches. How many seconds does it take for the radius of the balloon to increase from 3 inches to 5 inches?

NOTE: The volume of a sphere is 4/3*πr^3.

A. 6
B. 9
C. 24
D. 30
E. 42

If the radius of the balloon is 1 inch, the volume of the balloon is 4/3*π(1)^3 = 4π/3. If the radius is 2 inches, the volume is 4/3*π(2)^3 = 32π/3. Since it takes 3 seconds for the radius to increase from 1 inch to 2 inches, the rate at which the volume is increasing is (32π/3 - 4π/3)/3 = 28π/9 cubic inches per second.

Now, if the radius of the balloon is 3 inches, the volume of the balloon is 4/3*π(3)^3 = 108π/3. If the radius is 5 inches, the volume is 4/3*π(5)^3 = 500π/3. Since the rate at which the volume is increasing is 28π/9 cubic inches per second, then it takes (500π/3 - 108π/3)/(28π/9) = 392π/3 * 9/(28π) = 14 * 3 = 42 seconds to increase the radius of the balloon from 3 inches to 5 inches.

Answer: E
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