Question

Explain each step in the process of finding the area of a circle given the circumfrence

Answer 1

1. Divide the circumference by
   `2\pi`
2. Square the remaining number
3. Multiply the resulting value by
   `\pi`

Explanation:

Recall that the formula for the circumference of a circle is:

`2\pi r`

Also recall that the formula for the area of a circle is:

`\pi r^2`

Both formulas use the radius; one squares it, while the other doubles it.

Let's start by turning the formula for the circumference of a circle into the formula for the area of a circle. We start off with:

`2\pi r`

We want to square the radius, but we can't do that without squaring everything else, too, so let's get rid of the other terms.

Divide the circumference by
`2\pi`:

`2\pi r\\(2\pi r)/(2\pi ) =\\r`

Now, we can square r:

`r\\r^2`

Now, all we have to do is multiply by pi:

`r^2\\\pi r^2`

We now have the area.

Let's look back at out steps.

First, we divided the circumference by
`2\pi`.

Next, we squared the number we had left (the radius).

Finally, we multiplied by
`\pi`.