Answer:
[tex]\frac{225}{\pi }[/tex] or 71.6197
Step-by-step explanation:
This just manipulating formulas.
The formula for the circumference of a circle is [tex]2\pi r[/tex], and we know this is equal to 30. That means [tex]\pi r=15[/tex]. The formula for the area of a circle is [tex]\pi r^2[/tex], so we know the area of the circle must be [tex]15r[/tex] ([tex]\pi r*r[/tex], and we found [tex]\pi r[/tex] to be 15 earlier).
Now, using this information, let's find r in terms of [tex]\pi[/tex].
[tex]\pi r=15[/tex]
[tex]r=\frac{15}{\pi }[/tex]
Now let's plug in r to the expression we found for area.
[tex]15(\frac{15}{\pi } )[/tex]
[tex]\frac{225}{\pi }[/tex]
The area of the circle is approximately [tex]\frac{225}{\pi }[/tex] or 71.6197.
Edit- Apparently there is a formula for this:
[tex]\frac{c^{2} }{4\pi }[/tex] where [tex]c[/tex] is the circumference of the circle.
