   Chapter 11.4, Problem 23E ### 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

# Tumor growth For Problems 23 and 24, suppose that a tumor in a person’s body has a spherical shape and that treatment is causing the radius of the tumor to decrease at a rate of 1 mm per month.At what rate is the volume decreasing when the radius is 3 mm? ( Recall that  V  =  4 3 π r 3 . )

To determine

To calculate: The rate at which the volume is decreasing when the radius is 3 mm if a tumor in person’s body has a spherical shape and that treatment is causing the radius of tumor to decrease at a rate of 1 mm per month.

Explanation

Given Information:

The radius is 3 mm of a tumor in person’s body which has a spherical shape and the treatment is causing the radius of tumor to decrease at a rate of 1 mm per month.

Formula used:

Volume of a sphere of radius r is given by,

V=43πr3

Calculation:

As it is provided that the radius is 3 mm of a tumor in person’s body which has a spherical shape and the treatment is causing the radius of tumor to decrease at a rate of 1 mm per month.

Now, the volume of a sphere is,

V=43πr3

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

dVdt=4π

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