   Chapter 8.5, Problem 42E 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 41 and 42, round to two decimal places. A goat is tethered to a barn by a 12 -ft chain. If the chain is connected to the barn at a point 6 ft from one end of the barn, what is the area of the pasture that the goat is able to graze? To determine

To find:

The area of pasture that the goat will be able to graze.

Explanation

Formula:

If r is the radius of circle,

Acircle=πr2.

Calculation:

In the diagram shown below, the shaded area is the pasture that the goat will be able to graze.

The shaded area comprises of a quarter circle of radius 6 ft and a semicircle of radius 12 ft.

Let’s find the area of quarter circle. We know that Acircle=πr2.

Quarter circle is one-fourth part of the entire circle. Hence, the area of quarter circle of radius 6 ft will be 14×πr2.

Let’s substitute r=6 in the above equation to find the area of quarter circle.

Aquarter circle=14×π×62=14×π×36=9π ft2

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