To show the relationship between the circumference (C) and the area (A) of a circle, the correct expressions are:
- \( C = 2\pi r \) (This expression shows the circumference in terms of the radius \( r \).)
- \( A = \pi r^2 \) (This expression shows the area in terms of the radius \( r \).)
While both expressions reveal important aspects of circles, if you are looking for a direct expression that involves both \( C \) and \( A \), one can derive that:
- Using the two formulas above:
- The relationship between \( C \) and \( A \) can be computed using \( r \):
- From \( C = 2\pi r \), we can express \( r \) as \( r = \frac{C}{2\pi} \).
- Substituting \( r \) into the area formula gives \( A = \pi \left(\frac{C}{2\pi}\right)^2 = \frac{C^2}{4\pi} \).
So \( C^2 = 4\pi A \) is another relationship derived from \( C \) and \( A \).
Therefore, all expressions provided relate to circles, but the most fundamental ones are the last two:
- \( C = 2\pi r \)
- \( A = \pi r^2 \)
For expressing the relationship directly between circumference and area, \( C^2 = 4\pi A \) is derived from those fundamental expressions.