Chapter 5.2, Problem 56E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

Find the volume of the described solid *S*.

The base of *S* is the triangular region with vertices (0, 0), (1, 0), and (0, 1). Cross- sections perpendicular to the *y*-axis are equilateral triangles.

To determine

**To find:**

The volume of a solid S whose base is the triangular region with vertices *y*-axis are equilateral triangles.

Explanation

**1) Concept:**

Definition of volume:

Let S be a solid that lies between

**2) Given:**

Vertices of base triangle is

**3) Calculation:**

In the figure the base of cross section at

Then the height of the equilateral triangle (cross section) is

So the area of the triangle is

The equation of the line representing the diagonal is

That is

Therefore, at

The cross section are perpendicular to y-axis

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