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Elementary Geometry for College St...

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

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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A circle has an exact area of 27 π  ft 2 .

a) What is the area of a sector of this circle if the arc of the sector measures 80 ?

b) What is the exact perimeter of the sector in part (a)?

To determine

(a)

To find:

The area of a sector of the circle.

Explanation

Calculation:

Given:

The area of the circle = 27π ft2

The arc of the sector measures 80

The area of the circle A=πr2

πr2=27πr2=27r=27=33

Radius (r) = 33 ft.

Circumference=2πr=2π(33)=6π3

If x is the angle at the center obtained by the arc then the length of the arc is

To determine

(b)

To find:

The exact perimeter of the sector.

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