   Chapter 11, Problem 32RE ### 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

# Evaporation A spherical droplet of water evaporates at a rate of 1 mm 3 /min . Find the rate of change of the radius when the droplet has a radius of 2.5 mm.

To determine

To calculate: The rate of change of the radius when the droplet has a radius of 2.5 mm if the spherical droplet of water evaporates at a rate of 1 mm3/min.

Explanation

Given Information:

The spherical droplet of water evaporates at a rate of 1 mm3/min.

Formula Used:

As per the product rule, if two functions are given in the form f(x).g(x), then the derivative is given as:

ddx(f.g)=f.dgdx+g.dfdx

The rate is defined as the first derivative.

The volume of a sphere is given as:

V=43πr3, where r is the radius of the sphere.

Calculation:

The volume of the sphere is given as

V=43πr3.

Differentiate on both the sides with respect to t,

dVdt=[ddt(43πr3)]

Now apply the power rule of derivative,

dVdt=43πddt(r3)

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