   Chapter 9.3, Problem 45E 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

In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and H.A container of yogurt has the shape of a frustum of a cone. With the lower base having diameter length 6 cm and the upper base having diameter length 8 cm, the volume of such a container 7.5 cm tall can be determined by using H = 30 cm and h = 22.5 cm. Find its volume.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 find:

The volume of the container.

Explanation

Given:

A container of yogurt has the shape of the frustrum of a cone. With the lower base having diameter 6 cm and the upper base having diameter 8 cm, the volume of such a container 7.5 cm tall can be determined by using H=30 cm, h=22.5 cm.

Formula used:

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

Calculation:

We have r=3 cm, h=22.5 cm and R=4 cm, H=30 cm

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