Question

If the area of a circle is 114 cm squared, what is its circumference?

Answer 1

To calculate the circumference of a circle with an area of
`114` cm squared, start by finding the radius using the area formula and then apply it to the circumference formula, ensuring unit consistency and correct rounding for significant figures.

Step-by-step explanation:

To find the circumference of a circle when the area is given as
`114 cm2`, we can use the relationship between the area and the radius of the circle, which is
`A = πr2.`

First, we need to calculate the radius, and then we can use the circumference formula, which is
`C = 2πr.` Let's solve this step-by-step:

1. Solve for the radius,
   `r`, by rearranging the area formula:
   `r = √(A/π).`

2. Substitute the given area
   `(A = 114 cm2): r = √(114 cm2/3.1415927).`

3. Calculate the radius using a calculator (keeping significant figures in mind).

4. Now that the radius is known, use the circumference formula:

   
   `C = 2πr.`

5. Plug the radius into the formula to get the circumference.

Throughout the process, remember to keep units consistent and to round off the final answer to maintain the appropriate number of significant figures.