Chapter 5.2, Problem 51E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Find the volume of the described solid *S*.

A pyramid with height *h* and rectangular base with dimensions *b* and 2*b*

To determine

**To find:**

The volume of a pyramid with height

Explanation

**1) Concept:**

Definition of volume:

Let S be a solid that lies between

**2) Given:**

Height of pyramid is

**3) Calculations:**

Consider the pyramid having the apex point at the origin and its axis coinciding with the

From figure,

Consider the similar triangles,

For a cross-section at height

Using the properties of similar triangles,

That is,

Therefore, solving for

Similarly,

For a cross-section at height

Therefore, we have a rectangular cross section of width

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