Question

Eugene knows the circumference of a circle is 125.6 meters. Does he have enough information to find the area?

Answer 1

Yes, Eugene has enough information to find the area of the circle. The circumference of a circle is related to its radius through the formula:

\[
C = 2\pi r
\]

where \( C \) is the circumference and \( r \) is the radius. Given the circumference \( C = 125.6 \) meters, we can solve for the radius \( r \):

\[
125.6 = 2\pi r
\]

To isolate \( r \), divide both sides by \( 2\pi \):

\[
r = \frac{125.6}{2\pi}
\]

Now, we can use this radius to find the area \( A \) of the circle using the formula:

\[
A = \pi r^2
\]

Substituting \( r \) into the area formula:

\[
A = \pi \left( \frac{125.6}{2\pi} \right)^2
\]

Calculating \( A \):

1. Calculate \( \frac{125.6}{2\pi} \):

\[
r \approx \frac{125.6}{6.2832} \approx 20
\]
(using \( \pi \approx 3.14 \) for approximation, \( 2\pi \approx 6.2832 \))

2. Now find the area:

\[
A = \pi (20)^2 = \pi \times 400 \approx 1256 \text{ square meters}
\]

So, Eugene can indeed find the area of the circle which is approximately \( 1256 \) square meters.