Question

A circle has a circumference of 2 pi cm. Which statement about the circumference and area is true?

Answer 1

To analyze the situation, we first need to use the known formula for the circumference and area of a circle:

1. **Circumference (C)**: The circumference of a circle is given by the formula:
\[
C = 2 \pi r
\]
where \( r \) is the radius.

2. **Area (A)**: The area of a circle is given by the formula:
\[
A = \pi r^2
\]

Given that the circumference of the circle is \( 2 \pi \) cm, we can find the radius:

\[
2 \pi r = 2 \pi
\]
Dividing both sides by \( 2 \pi \):
\[
r = 1 \text{ cm}
\]

Now, we can find the area using the radius we've just calculated:
\[
A = \pi r^2 = \pi (1)^2 = \pi \text{ cm}^2
\]

Now we have:
- Circumference \( C = 2 \pi \) cm
- Area \( A = \pi \) cm²

### Comparison of Circumference and Area:
To analyze the relationship:
- The circumference \( C = 2 \pi \).
- The area \( A = \pi \).

It's clear that \( C \) is greater than \( A \):
\[
C = 2 \pi > \pi = A
\]

Thus, the true statement about the circumference and area is:
**The circumference is greater than the area.**