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