   Chapter 11.4, Problem 31E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Volume and radius Suppose that air is being pumped into a spherical balloon at a rate of 5 in 3 /min . At what rate is the radius of the balloon increasing when the radius is 5 in.?

To determine

To calculate: The rate at which the radius of balloon is increasing when the radius is 5 in. and the air is being pumped into a spherical balloon at a rate of 5 in3/min.

Explanation

Given Information:

The air is being pumped into a spherical balloon at a rate of 5 in3/min.

Formula used:

The volume of a sphere of radius r is given by,

V=43πr3

Calculation:

The volume of a sphere of radius r is given by,

V=43πr3

To obtain the rate of change of volume, differentiate above equation with respect to t as,

dVdt=4πr2drdt

Now, as the radius is 5 in

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