The area of a circle can be calculated with the following formula:
[tex]A=\pi r^2[/tex]Where "r" is the radius of the circle.
In this case, you know that the area of the circular piece of cardboard is:
[tex]A=200\operatorname{cm}^2[/tex]Then, knowing the area, you can substitute it into the formula:
[tex]200\operatorname{cm}^2=\pi r^2[/tex]Finally, you have to solve for "r" in order to find the radius. Rounded to the nearest Whole number, the radius is:
[tex]r\approx8\operatorname{cm}[/tex]