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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

Elementary Geometry For College St...

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

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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