Evie measured the circumference of a circle. Which steps can she follow to find the area of the circle?

A.
Multiply the circumference by
π
to find the diameter. Multiply the diameter by 2 to find the radius. Use the radius in the formula
A
=
π
r
2
to find the area.

B.
Divide the circumference by
π
to find the diameter. Divide the diameter by 2 to find the radius. Use the radius in the formula
A
=
2
π
r
to find the area.

C.
Divide the circumference by
π
to find the diameter. Divide the diameter by 2 to find the radius. Use the radius in the formula
A
=
π
r
2
to find the area.

D.
Multiply the circumference by
π
to find the diameter. Multiply the diameter by 2 to find the radius. Use the radius in the formula
A
=
2
π
r
to find the area.

1 answer

To find the area of a circle from its circumference, you can follow these steps:

  1. Find the diameter using the formula for circumference:
    \[ C = \pi d \] Therefore, the diameter can be found by dividing the circumference by \(\pi\):
    \[ d = \frac{C}{\pi} \]

  2. Find the radius by dividing the diameter by 2:
    \[ r = \frac{d}{2} = \frac{C}{2\pi} \]

  3. Use the radius to find the area using the area formula:
    \[ A = \pi r^2 \]

Given these steps, the correct option is:

C. Divide the circumference by \(\pi\) to find the diameter. Divide the diameter by 2 to find the radius. Use the radius in the formula \(A = \pi r^2\) to find the area.