BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.4, Problem 94E
To determine

Find the time at which the snowball to melt completely.

Expert Solution

Answer to Problem 94E

It takes 3 more hours to lose the other half of the volume.

Explanation of Solution

Given:

The volume of snowball decreases at a rate proportional to its surface area and takes three hours to decrease to half its original volume.

Calculation:

From the given statement, the rate of change of the volume is proportional to the surface area.

  dVdt=cA , where c is a constant.

Use formula of sphere.

  V=43πr3

  A=4πr2

Now,

  ddt(43πr3)=c(4πr2)43πddt(r3)=c(4πr2)43π3r2drdt=c(4πr2)drdt=c

Hence it takes 3 more hours to lose the other half of the volume.

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