Chapter 5.2, Problem 52E

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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 base an equilateral triangle with side *a* (a tetrahedron)

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 triangle consisting of two vertices of the base and the center of the base.

This triangle is similar to the corresponding triangle at a height y,

So from the figure,

Also, by similar triangles,

These two equations imply that

Since the cross section is an equilateral triangle, it has area

After substituting the value of

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