Find the area of a circle given C=4π. Give your answer in terms of π.
(1 point)
C = 2 pi r = 4 pi so r = 2
A = pi r^2 = pi * 2^2 = 4 pi
LOL, same numbers as circumference
Yes, that's correct! The area of the circle is 4π.
To find the area of a circle given the circumference (C=4π), you can use the following formula:
C = 2πr
where C is the circumference and r is the radius of the circle.
We are given C = 4π. By substituting this value into the formula, we can solve for the radius:
4π = 2πr
Dividing both sides of the equation by 2π:
2 = r
Now that we know the radius is 2, we can use the formula for the area of a circle:
A = πr²
Substituting the radius into the formula:
A = π(2)²
Simplifying:
A = π * 4
The area of the circle is 4π, which is the final answer.
To find the area of a circle, we need to use the formula:
A = π * r^2
where A represents the area of the circle, π is a constant approximately equal to 3.14, and r is the radius of the circle.
In this case, we are given the circumference, C, which is related to the radius by the formula:
C = 2 * π * r
We can rearrange this formula to solve for the radius, r:
r = C / (2 * π)
Given that C = 4π, we substitute this value into the formula for r:
r = (4π) / (2 * π)
= 2
Now that we know the radius is 2, we can use this value to find the area of the circle:
A = π * r^2
= π * 2^2
= 4π
So, the area of the circle, given C = 4π, is 4π square units.