How do I find a formula for the area of a circle with a circumference c?
C = pi * d
C=2pi*r
(1/2)C=(1/2)(2pi*r)
(1/2)C=pi*r
(1/2)C*r = pi*r^2 =A
To find a formula for the area of a circle with a given circumference c, you can use the formula for the circumference of a circle:
c = 2πr,
where c represents the circumference and r represents the radius of the circle.
To find the radius, you can rearrange the formula:
r = c / (2π).
Once you have the radius, you can use the formula for the area of a circle:
A = πr^2
where A represents the area and r is the radius.
Substitute the value of the radius (c / (2π)) into the area formula to get:
A = π(c / (2π))^2
Simplify the expression:
A = π(c^2 / 4π^2)
Cancel out the π terms:
A = c^2 / (4π)
Therefore, the formula for the area of a circle with a given circumference c is A = c^2 / (4π).