Question

Formulas for the area, A. and the circumference, C, of a circle in terms of the radius. r. are shown. A =TTY2 C=2TTT Use the formulas to create an equation that expresses the area of a circle in terms of the circumference. Move the correct answer to each box 2 4 C 21 c (( 2 A = 1 Il

Answer 1

The area of a circle is given by:

`A=\pi r^2`

and the circunference is given by:

`C=2\pi r`

So we can solve the equation of the circunference for r so:

`r=(C)/(2\pi)`

Now we can replace this expression for r in the area equation so:

`A=\pi((C)/(2\pi))^2`

and finally we simplify it so:

`A=(\pi C^2)/(4\pi^2)=(C^2)/(4\pi)`