Answer:
[tex]A=\frac{225t^2}{\pi}[/tex] given the circumference is 30t.
Step-by-step explanation:
The circumference of a circle is [tex]C=2\pi r[/tex] and the area of a circle is [tex]A=\pi r^2[/tex] assuming the radius is [tex]r[/tex] for the circle in question.
We are given the circumference of our circle is [tex]2 \pi r=30t[/tex].
If we solve this for r we get: [tex]r=\frac{30t}{2\pi}[/tex]. To get this I just divided both sides by [tex]2\pi[/tex] since this was the thing being multiplied to [tex]r[/tex].
So now the area is [tex]A=\pi r^2=\pi (\frac{30t}{2 \pi})^2[/tex].
Simplifying this:
[tex]A=\pi (\frac{30t}{2 \pi})^2[/tex].
30/2=15 so:
[tex]A=\pi (\frac{15t}{\pi})^2[/tex].
Squaring the numerator and the denominator:
[tex]A=\pi (\frac{(15t)^2}{(\pi)^2}[/tex]
Using law of exponents or seeing that a factor of [tex]\pi[/tex] cancels:
[tex]A=\frac{(15t)^2}{\pi}[/tex]
[tex]A=\frac{15^2t^2}{\pi}[/tex]
[tex]A=\frac{225t^2}{\pi}[/tex]
