Chapter 5.R, Problem 23E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the base.

To determine

**To find:**

The volume of the solid S where parallel cross sections perpendicular to the base are isosceles triangles with hypotenuse lying along the base.

Explanation

**1) Concept:**

Use the definition of volume.

**2) Definition of volume:**

Let S be a solid that lies between

**3) Calculations:**

Fig (a) represents the graph of a circle that is the base of solid S and has radius

The red line

From fig (a), the hypotenuse of the triangle can be found by finding the distance between the top half of the circle and the

The equation of circle with radius

Solving for

From fig (a),

Hypotenuse

Now, find the length of the other two sides of an isosceles triangle by Pythagoras theorem.

Since it is an isosceles triangle, length of the other two sides is equal.

Therefore, substitute

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