Question

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

Answer 1

`(225)/(\pi )` or 71.6197

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=(15)/(\pi )`

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

`15((15)/(\pi ) )`

`(225)/(\pi )`

The area of the circle is approximately
`(225)/(\pi )` or 71.6197.

Edit- Apparently there is a formula for this:

`(c^(2) )/(4\pi )` where
`c` is the circumference of the circle.