   Chapter 9.4, Problem 49E 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

Explain how the following formula used in Example 6 was obtained: V = 4 3 π R 3 - 4 3 π r 3

To determine

To find:

The explanation for the formula V=43πR3-43πr3, used in Example 6.

Explanation

Approach:

A sphere is a three dimensional solid figure, which is made up of all the points in space, which lie at a common distance, called the radius, from a fixed point called the center of the sphere. The surface area of a sphere S=4πr2, where r is the radius of the sphere.

All solid bodies occupy space. The measure of occupied space is called the volume of the object. Volume of a sphere = V = 43πr3.

Concentric spheres have the same center but different radii.

Calculation:

Consider a hollow plastic ball, where the inside diameter of the ball and the thickness of the ball is given. To calculate the volume of material needed to construct the ball, we will use the concept of concentric spheres.

The difference in the volume of the outside sphere and the inside sphere gives us the volume of the material needed to construct the ball

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