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If the diameter of circle C is 4inches, how do I find the area of the shaded sector ACB?

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hardworking-h... | eNoter

Posted June 8, 2013 at 3:34 PM via web

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If the diameter of circle C is 4inches, how do I find the area of the shaded sector ACB?

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Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted June 8, 2013 at 3:51 PM (Answer #1)

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Notice that the measure of the central angle of the shaded sector is 90 degrees. It means that it divide the circle by 4.

So, to solve for its area, apply the formula of area of circle.

`A= pir^2`

Since radius is half of the diameter, then:

`A_(c ir c l e)=pi(4/2)^2=pi(2)^2=4pi`

Then, divide divide it by 4.

`A_(ACB)=(4pi)/4=pi`

 

Or, apply the formula of area of sector which is:

`A= 1/2 r^2 theta`

where `theta` is the central angle of the sector in radians.

Since `90^o=pi/2` , then:

`A_(ACB)=1/2(4/2)^2*pi/2= 1/2*2^2*pi/2=1/2*4*pi/2 = pi`

 

Hence, the area of the shaded sector is `pi` square inches.

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