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in a circle, a 90 degree sector has area 16 ft squared. What is the radius of the circle?

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2 Answers

Autumn  -

Since a circle has 360 degrees, a 90 degree sector is 1/4 of the circle. Therefore, the area of the entire circle can be expressed as

Area of sector/Size of sector = Area of Circle/360

16 ft2/90 = n/360

(360) (16 ft2)/90 = n

(4)(16 ft2) = n

n = 64 ft2 is the area of the entire circle.

Now since Area of a Circle = ∏r2,

∏r2 = 64

r2 = 64/∏

r = √(64/∏)

Rationalizing the denominator, we multiply by √∏/√∏ to get

r = √(64∏)/√(∏2) and taking the square root of the denominator to get our answer of

r = √(64∏)/∏

 

Let's start off with the formula for the area of a circle:

A=πr2. A great way to remember this is to combine it with the circumference formula (C=πd) in a saying that goes like this: Cherry Pie is Delicious, Apple Pies aRe Too. 

In any circle we have 360º around. If we know that in 90º the area is 16ft2, and 90 is 1/4 of 360, then we take the 16ft2 and multiply it by 4 to get the area of the whole circle. 

16*4=64ft2. Now all we do is plug this into the area equation and solve for r.

64=πr2 -> 64/π=r2 -> √(64/π)=r. Answer. You can now plug that into a calculator to get the definite answer. 

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