Question

Find the circumference of a circle with an area of 95.03 m^2. Round the answer to the nearest tenth.

Answer 1

Step-by-step explanation

Area and circumference

The area of a circle with radius r is given by the following formula:

`A=\pi r^2`

The circumference of that circle is given by:

`C=2\pi r`

Finding the answer

We are given the area of the circle. With this data and the first formula we can construct an equation for the radius r. Once we find the radius of the circle we can use it to find its circumference. So first of all we take the first formula and we equalize it to 95.03:

`95.03=\pi r^2`

We can divide both sides by π:

`\begin{gathered} (95.03)/(\pi)=(\pi r^2)/(\pi) \\ r^2=(95.03)/(\pi) \end{gathered}`

Now we apply a square root to both sides:

`\begin{gathered} √(r^2)=\sqrt{(95.03)/(\pi)} \\ r=\sqrt{(95.03)/(\pi)} \end{gathered}`

And that's the radius of the circle. Then we can use this value in the formula of the circumference C:

`C=2\pi *\sqrt{(95.03)/(\pi)}=34.6`

Answer

Then the answer is 34.6 m.