Question

If the area of a circle is 114cm squared, what is it’s circumference ?

Answer 1

See a solution process below:

Explanation:

First, we need to determine the radius of the circle.

The formula for the area of a circle is:

`A = pir^2`

We can substitute `114"cm"^2` for `A` which is given in the problem.

And, we can approximate `pi` with `3.14`

Substituting and solve for `r` gives:

`114"cm"^2 = 3.14r^2`

`(114"cm"^2)/color(red)(3.14) = (3.14r^2)/color(red)(3.14)`

`36.31"cm"^2 = (color(red)(cancel(color(black)(3.14)))r^2)/cancel(color(red)(3.14))`

`36.31"cm"^2 = r^2`

`sqrt(36.31"cm"^2) = sqrt(r^2)`

`6.03"cm" = r`

`r = 6.03"cm"`

Now that we know the radius of the circle we can determine it's circumference. The formula for the circumference of a circle is:

`C = 2pir`

We will again use `3.14` to approximate `pi` and substitute the radius we calculated above. Substituting and calculating `C` gives:

`C = 2 * 3.14 * 6.03"cm"`

`C = 6.28 * 6.03"cm"`

`C = 37.87cm"`

The circumference of the circle is approximately 37.87 centimeters