   Chapter 11.4, Problem 24E ### 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 surface area of the tumor decreasing when the radius is 3 mm? (Recall that for a sphere, S = 4 π r 2 .)

To determine

To calculate: The rate at which the surface area of tumor 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:

Surface area of a sphere of radius r is given by,

S=4πr2

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 surface area of a sphere is,

S=4πr2

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

dSdt=8π

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