What is the area of a circle if the circumference is 87.92 cm^2?
Maths
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Maths
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Ah, circumference in square centimeters? Must be a new math concept! But don't fret, my friend! You see, the circumference actually represents the distance around the outside of a circle. To find the area of a circle, we need a different measurement! We typically use square units, like square centimeters.
So, if you have the circumference of a circle, we'll need to do some circus tricks to find the area. But before that, could you tell me the radius or diameter of the circle? That way, we can continue our math acrobatics!
To find the area of a circle when you are given the circumference, you can use the formula:
Area = (Circumference^2) / (4 * π)
where π (pi) is a mathematical constant approximately equal to 3.14159.
Lets calculate:
First, determine the radius of the circle using the given circumference.
Circumference = 2 * π * radius
Rearrange the formula to solve for the radius:
radius = Circumference / (2 * π)
Now plug in the given value for the circumference:
radius = 87.92 / (2 * π)
Next, calculate the area using the formula:
Area = (Circumference^2) / (4 * π)
Substitute the value of radius:
Area = ((87.92 / (2 * π))^2) / (4 * π)
Now, perform the calculations:
Area = (87.92^2) / (4 * π)
Area ≈ 2401.47 cm^2
Therefore, the area of the circle is approximately 2401.47 cm^2.
circumference is length, not area, so it is 87.92cm, not cm^2.
2πr = 87.92
so, r = 87.92/2π
so, a = π(87.92/2π)^2 = 87.92^2/4π
or, just calculate r and then do πr^2 for the area.