Question

Question

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

C=2πr
upper C equals 2 pi r

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

A=πr2
upper A equals pi r squared

Cd=π

Answer 1

The correct expressions that show the relationship between the circumference and the area of a circle are:

1. \( C = 2\pi r \) (Circumference in terms of radius)
2. \( A = \pi r^2 \) (Area in terms of radius)

Among the options you provided, the expression that directly relates the circumference and area is not explicitly shown. However, you can derive a connection using both relationships.

The area (A) can be expressed in terms of the circumference (C) as follows:

1. From \( C = 2\pi r \), we can express \( r \) as: \[ r = \frac{C}{2\pi} \]

2. Substituting \( r \) into the area formula \( A = \pi r^2 \): \[ A = \pi \left(\frac{C}{2\pi}\right)^2 \] \[ A = \pi \cdot \frac{C^2}{4\pi^2} \] \[ A = \frac{C^2}{4\pi} \]

So the expression \( C^2 = 4\pi A \) is indeed a correct relationship derived from the circumference and area. Therefore, among your options, the expression \( C^2 = 4\pi A \) is key in connecting circumference and area.