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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 6, Problem 5P

To determine

**To show:** The depth of the water decreases at a constant rate without regarding the shape of the bowl.

Expert Solution

The depth of the water decreases at a constant rate.

**Given information:**

Water in an open bowl evaporates at a rate proportional to the area of the surface of the water.

**Calculation:**

The rate of decrease of the volume is proportional to the area of the surface.

Here, *k* is the positive constant and *x*.

Consider that the rate of change of depth with respect to time as

Apply Chain rule as shown below.

Substitute

Expression for the volume of water up to a depth *x* as shown below.

Here, *s*.

Differentiate both sides of the Equation with respect to *x*.

Substitute

Therefore, the depth of the water decreases at a constant rate without regarding the shape of the bowl. Hence, it is proved.