   Chapter 9.3, Problem 43E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A frustum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base. With dimensions are indicated, show that the volume of the frustum of the cone is V = 1 3 π R 2 H − 1 3 π r h 2

To determine

To show:

The volume of the frustum of the cone is V=13πR2H13πr2h.

Explanation

Given:

A frustrum of a cone is the portion of the cone bounded between the circular base and a plane parallel to the base.

Formula used:

The volume of the circular cone is V=13πr2h.

Calculation:

The frustum of the cone is constructed by cutting a smaller circular cone away from the larger cone.

Let R and H be the radius and height of the larger cone.

Then its volume is V1=13πR2H.

Let r and h be the radius and height of the smaller cone.

Then its volume is V2=13πr2h

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