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Math
GeometryElementary Geometry for College Students6th Edition

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Chapter 9.3, Problem 45E
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Elementary Geometry for College St...

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

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Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
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=13πR2H−13πr2h.

Calculation:

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

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