Chapter 15.1, Problem 6E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

A 20-ft-by-30-ft swimming pool is filled with water. The depth is measured at 5-ft intervals, starting at one corner of the pool, and the values are recorded in the table. Estimate the volume of water in the pool.

To determine

**To estimate:** The volume of water in the swimming pool of dimension

Explanation

**Formula used:**

The volume of water in the pool is,

Where,
*a* is the length of the side of the square.

The Riemann sum constants are *m*, *n*.

**Given:**

The surface,

The rectangular region,

**Calculation:**

Let the Riemann sum partitions be

Plot the given rectangle in the graph and pick the sample points at the upper right corners of each square.

From Figure 1, it is observed that the upper right corners of each square is

Therefore,

From the given table, it is observed that,

The value corresponds to

The value corresponds to

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