   Chapter 8.5, Problem 43E 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

An exit ramp from one freeway to another freeway forms a 900 arc of a circle. The ramp is scheduled for resurfacing. As shown, its inside radius is 370 ft, and its outside radius is 380 ft. What is the area of the ramp to the nearest integer? To determine

To find:

The area of the ramp to the nearest integer.

Explanation

Formula:

Area of sector:

If r is the radius of the circle, the area A of a sector whose arc has degree measure m is given by

A=m360×πr2.

Calculation:

To find the area of the ramp, we have to subtract the area of inner sector with radius 370 ft. from the area of outer sector with radius 380 ft.

Area of the ramp =Aouter sector-Ainner sector

It is given that the ramp forms an arc of 900.

Let’s find the area of outer sector.

From the diagram, it is clear that the radius of outer sector is 380 ft.

Let’s substitute the value of radius (380 ft) of outer sector and m=900 to find the area of outer sector.

Asector=m360×πr2

Aouter sector=90360×π×3802

Simplify:Aouter sector=14×π×144400

Simplify: Aouter sector=36100π ft2

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