What is the radius in cm of the equivalent circular field for a 10 cm x 10 cm square field?

To determine the radius of the equivalent circular field for a square field, we first need to calculate the area of the square. A square that measures 10 cm by 10 cm has an area of 100 cm² (since area = side length x side length).

Next, we need to use the formula for the area of a circle, which is given by the equation A = πr², where A is the area and r is the radius. To find the radius that corresponds to the same area as the square, we set the area of the circle equal to the area of the square:

πr² = 100 cm²

Solving for r, we first isolate r²:

r² = 100 cm² / π

To find r, we take the square root of both sides:

r = √(100 cm² / π)

As π is approximately 3.14, this value can be approximated as follows:

r ≈ √(31.83) ≈ 5.64 cm.

The question requests the radius in centimeters, and the closest whole number option to this result is 5 cm. This corresponds to the radius of the equivalent circular field that has the same area as a