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

Responses

A=πr2
upper A equals pi r squared

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

C=2πr
upper C equals 2 pi r

C2=4πA

He

1 answer

To find the correct expression that shows the relationship between the circumference and the area of a circle, let's analyze the options:

  1. A = πr²: This is the formula for the area of a circle.
  2. Cd = π: This appears to be incorrect notation. The correct relationship is that \( C = πd \) where \( C \) is circumference and \( d \) is diameter.
  3. C = 2πr: This is the formula for the circumference of a circle.
  4. C² = 4πA: This relationship is correct since, if you substitute \( A = πr² \) into the equation, you can derive the relationship between circumference and area.

The correct expressions that show the relationship would be the combination of the area formula and the circumference formula, leading us to option 4, C² = 4πA.

So the best responses showing relationships between circumference and area would include:

C = 2πr (circumference)
A = πr² (area)
C² = 4πA (relationship derived from the two)

If you’re selecting only one option that best exemplifies the relationship between circumference and area, then C² = 4πA is the most appropriate choice.