Question

The circumference of a circular garden is approximately 30 feet. What is the approximate area inside the circular garden?

Answer 1

Answer:

$\frac{225}{\pi }$ or 71.6197

Step-by-step explanation:

This just manipulating formulas.

The formula for the circumference of a circle is $2\pi r$, and we know this is equal to 30. That means $\pi r=15$. The formula for the area of a circle is $\pi r^2$, so we know the area of the circle must be $15r$ ($\pi r*r$, and we found $\pi r$ to be 15 earlier).

Now, using this information, let's find r in terms of $\pi$.

$\pi r=15$

$r=\frac{15}{\pi }$

Now let's plug in r to the expression we found for area.

$15(\frac{15}{\pi } )$

$\frac{225}{\pi }$

The area of the circle is approximately $\frac{225}{\pi }$ or 71.6197.

Edit- Apparently there is a formula for this:

$\frac{c^{2} }{4\pi }$ where $c$ is the circumference of the circle.