It's in geometry.

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

# 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 ft^{2}/90 = n/360

(360) (16 ft^{2})/90 = n

(4)(16 ft^{2}) = n

n = 64 ft^{2 }is the area of the entire circle.

Now since Area of a Circle = ∏r^{2},

∏r^{2} = 64

r^{2} = 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=πr^{2}. 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 16ft^{2}, and 90 is 1/4 of 360, then we take the 16ft^{2} and multiply it by 4 to get the area of the whole circle.

16*4=64ft^{2}. Now all we do is plug this into the area equation and solve for r.

64=πr^{2} -> 64/π=r^{2} -> √(64/π)=r. Answer. You can now plug that into a calculator to get the definite answer. ^{
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