Chapter 9.3, Problem 29E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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A triangle has sides that measure

*(HINT: The altitude to the 25-cm side has length 12 cm.)*

To determine

**To find:**

The exact volume of the solid of revolution formed when the triangle is rotated.

Explanation

**Given:**

A triangle has sides that measure 15 cm, 20 cm, and 25 cm. A solid is formed when the triangle is revolved about the side of length 25 cm. The altitude to the 25-cm side has length 12 cm.

**Formula used:**

The volume of the right circular cone is

**Calculation:**

Rotate the triangle is rotated about its 25-cm side. The altitude to the 25-cm side has length 12 cm.

Let *ABC* be the right triangle with

From the figure we see that the solid formed by rotation is the union of two right circular cones.

Given that the altitude to the 25-cm side has length 12 cm.

Therefore,

Now rotate the triangle *CDB* about *CD*, we get a right circular cone with altitude *CD* and base radius 12 cm.

The volume of the right circular cone formed is

Now rotate the triangle *ADB* about *AD, *we get a right circular cone with altitude *AD* and base radius 12 cm.

The volume of the right circular cone formed is

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