Question

Olivia is told that the circumference of a circle is equal to 8π
. How can she use this value to calculate the area of the circle without first finding the radius of the circle?(1 point)
Responses

Olivia should divide the given circumference by 4π
and then square the result to find the area of the circle.
Olivia should divide the given circumference by 4 pi and then square the result to find the area of the circle.

Olivia should divide the given circumference by 4π
to find the area of the circle.
Olivia should divide the given circumference by 4 pi to find the area of the circle.

Olivia should divide the given circumference by 2π
to find the area of the circle.
Olivia should divide the given circumference by 2 pi to find the area of the circle.

Olivia should square the given circumference and then divide by 4π
to find the area of the circle.

Answer 1

is it





You're very close! You've got the right idea of dividing the circumference by something, but the number is slightly off.

Remember, we want to use the formula:

A
=
C
2
4
π
A=
4π
C
2

​

So, Olivia should square the given circumference and then divide by 4π to find the area of the circle.

Answer 2

To find the area of the circle using the given circumference, Olivia can use the relationship between circumference and area. The formulas are:

- Circumference (C) = \(2\pi r\)
- Area (A) = \(\pi r^2\)

Given that the circumference is \(8\pi\), we can find the radius using the circumference formula:

1. Set the circumference equal to \(8\pi\):
\[
2\pi r = 8\pi
\]

2. Divide both sides by \(2\pi\):
\[
r = \frac{8\pi}{2\pi} = 4
\]

3. Now, substitute \(r = 4\) into the area formula:
\[
A = \pi r^2 = \pi (4)^2 = 16\pi
\]

However, Olivia can directly find the area without calculating the radius by noticing that:

1. The area can also be found using the circumference directly:
\[
A = \frac{C^2}{4\pi}
\]

Substituting \(C = 8\pi\):
\[
A = \frac{(8\pi)^2}{4\pi} = \frac{64\pi^2}{4\pi} = 16\pi
\]

Thus, the correct way for Olivia to find the area without finding the radius first is:

**Olivia should divide the given circumference by \(4\pi\) and then square the result to find the area of the circle.**

So the response would be:

"Olivia should divide the given circumference by \(4\pi\) and then square the result to find the area of the circle."