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I have answer of this question, but I want to learn how to get the answer. This is a culculus problem.
A spherical balloon is inflated with gas at the rate of 20 cubic feet per minute. How fast is the radius is (a) 1 foot and (b) 2 feet?
Answer: (a) 5/pie as 3.14
(b) 5/4pie as 3.14

2007-11-06 13:23:26 · 2 answers · asked by Anonymous in Science & Mathematics Mathematics

2 answers

The volume V of a sphere is given by

V = (4/3)πr³

Differentiate both sides with respect to t:

dV/dt = (4/3)π * 3r² dr/dt = 4πr² dr/dt

So

dr/dt = (dV/dt)/(4πr²)

You are given that dV/dt = 20, so you should now be able to determine the value of dr/dt for any radius r.

2007-11-06 13:36:54 · answer #1 · answered by Ron W 7 · 0 0

Hard one maybe some geniuses know.

2007-11-06 21:30:24 · answer #2 · answered by Anonymous · 0 1

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