   Chapter 9.3, Problem 29E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 25 cm.(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 V=13πr2h.

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 AB=15,BC=20,AC=25.

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, BD=12 cm.

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 V1=13π(12)2CD.

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 V2=13π(12)2AD

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