Answer:
C^2 = 4πA
Step-by-step explanation:
The first part asks us to isolate r in the equation C = 2πr. We can do that by dividing both sides by C: [tex]r=\frac{C}{2\pi }[/tex]. Note that C stands for the circumference of a circle.
The second step is to plug this value of r into the formula for the area of a circle. We know that the area of a circle is πr^2. We are given π and the exponent, so we just need to plug in [tex]\frac{C}{2\pi }[/tex] and we end up getting [tex]A=\pi (\frac{C}{2\pi })^{2}[/tex]
The third step is to square the term in the parentheses. Whenever we have to square a fraction, all we have to do is square the numerator and the denominator:
[tex](\frac{C}{2\pi })^2=\frac{C^2}{(2\pi )^2}=\frac{C^2}{2^2\pi ^2}[/tex]
In other words,
[tex]A=\pi *\frac{C^2}{2^2\pi ^2}[/tex]
For the fourth step, 2^2 can be evaluated to get 4. We end up getting the following if we do this:
[tex]A=\frac{\pi}{4 } *\frac{C^2}{\pi^2}[/tex]
For the fifth step, we can simplify because the π in the numerator of the first fraction and the π^2 in the denominator of the second fraction cancel (π^2 / π leaves π in the denominator and a 1 in the numerator). If we perform this cancellation, we get the following fraction:
[tex]A=\frac{C^2}{4*\pi}[/tex]
For the final step, we can isolate C^2 by multiply both sides by 4π. Then, we get that C^2 = 4πA
In other words, the circumference of the circle squared is equal to 4π times the area of the circle
