A spherical balloon is inflating with helium at a rate of 128 ft³/min. How fast is the balloon's radius increasing at the instant the radius is 4 ft? How fast is the surface area increasing? The balloon's radius is increasing at a rate of (Simplify your answer.) ft/minat the instant the radius is 4ft. The surface area is increasing at a rate of ☐ ft²/min at the instant the radius is 4 ft. (Type an exact answer, using as needed.)

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 45SE: A driver of a car stopped at a gas station to fill up his gas tank. He looked at his watch, and the...
Question
A spherical balloon is inflating with helium at a rate of 128 ft³/min. How fast is the balloon's radius increasing at the instant the radius is 4 ft? How fast is the surface area increasing?
The balloon's radius is increasing at a rate of
(Simplify your answer.)
ft/minat the instant the radius is 4ft.
The surface area is increasing at a rate of ☐ ft²/min at the instant the radius is 4 ft.
(Type an exact answer, using as needed.)
Transcribed Image Text:A spherical balloon is inflating with helium at a rate of 128 ft³/min. How fast is the balloon's radius increasing at the instant the radius is 4 ft? How fast is the surface area increasing? The balloon's radius is increasing at a rate of (Simplify your answer.) ft/minat the instant the radius is 4ft. The surface area is increasing at a rate of ☐ ft²/min at the instant the radius is 4 ft. (Type an exact answer, using as needed.)
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