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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

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

Chapter 9.3, Problem 45E, In Exercises 44 and 45, use the formula from Exercise 43. Similar triangles were used to find h and

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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