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:

$r=\frac{C}{2\pi}$

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

$A=\pi(\frac{C}{2\pi})^2$

and finally we simplify it so:

$A=\frac{\pi C^2}{4\pi^2}=\frac{C^2}{4\pi}$