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Solved: The radius of an inflating balloon A spherical
Chapter 3, Problem 31E(choose chapter or problem)
The radius of an inflating balloon A spherical balloon is inflated with helium at the rate of 100? ft3/min. How fast is the balloon’s radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing?
Questions & Answers
QUESTION:
The radius of an inflating balloon A spherical balloon is inflated with helium at the rate of 100? ft3/min. How fast is the balloon’s radius increasing at the instant the radius is 5 ft? How fast is the surface area increasing?
ANSWER:Solution Step 1 of 2: 3 We have given a spherical balloon is inflated with helium at the rate of 100 ft /minand also radius is given which is 5 ftwe have to find the rate of increasing surface area We have volume of the spherical balloon is V = r3 3 dV = 4r 2dr dt dt 100 = 4(5) 2dr ( dV = 100 ft /min,r = 5 ft) dt dt dr 2 dt = 1 ft /min. dV 2dr dt = 4r dt