Chapter 15.3, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A swimming pool is circular with a 40-ft diameter. The depth is constant along east-west lines and increases linearly from 2 ft at the south end to 7 ft at the north end. Find the volume of water in the pool.

To determine

**To find:** The volume of water in the swimming pool.

Explanation

**Given:**

The swimming pool is in circular shape of diameter 40 ft.

**Formula used:**

If *R* given by

If

**Calculation:**

Since the swimming pool is in the circular shape, *r* varies from 0 to 20 and

Substitute the values in the equation *a* and *b.*

Case (i):

Case (ii):

Solve the equations (3) and (4). That is, add both the equations yields,

And, substitute the value of *b* in the equation (3),

Therefore,

Integrate the function with respect to *r* and

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