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

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lemjay | High School Teacher | (Level 3) Senior Educator

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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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