Question

Which of the following expressions correctly shows the relationship between the circumference and the area of a circle?(1 point)
Responses

C2=4πA
upper C squared equals 4 pi upper A

A=πr2
upper A equals pi r squared

Cd=π
Start Fraction upper C over d End Fraction equals pi

C=2πr

Answer 1

The relationship between the circumference (C) and the area (A) of a circle is best represented by the following equations:

- The circumference of a circle is given by: \( C = 2\pi r \)
- The area of a circle is given by: \( A = \pi r^2 \)

Among the options provided, you have:

1. \( C^2 = 4\pi A \) (This is correct and relates circumference to area, derived from the formulas.)
2. \( A = \pi r^2 \) (This is a correct and standard formula for the area of a circle.)
3. \( \frac{C}{d} = \pi \) (This relates circumference to diameter and is also correct.)
4. \( C = 2\pi r \) (This is the standard formula for the circumference of a circle.)

All four options express relationships related to a circle, but if you're specifically asking for those that show direct relationships between circumference and area, option 1: \( C^2 = 4\pi A \) is the best representation.

So, to summarize:
- All expressions are valid but the one that directly describes a relationship between circumference and area is **C² = 4πA**.