   Chapter 9.4, Problem 37E 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

A leather soccer ball has an inside diameter length of 8.5 in. and thickness of 0.1 in. Find the volume of leather needed for its construction. Use your calculator.

To determine

To find:

The volume of the leather needed to construct a soccer ball.

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 is V=43πr3.

Calculation:

Consider a leather soccer ball.

The inside diameter of the soccer ball =8.5 in and the thickness of the soccer ball =0.1 in.

The volume of leather needed to construct the soccer ball is the difference between the outside volume and the inside volume of the ball.

Let r denotes the length of the inside radius, (r) =8.52=4.25 in.

Let R denotes the length of the outside radius,

(R) = (length of inside radius(r) + thickness).

R=4

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