To find the radius of a circle that circumscribes a square, we first need to understand the relationship between the square and the circle. An inscribed square touches the circle at its corners.
Given that the side length of the square is 8 inches, we can find the radius of the circumscribing circle using the formula:
Radius = (Diagonal of the square) / 2
The diagonal (d) of the square can be calculated using the Pythagorean theorem:
d = √(side² + side²) = √(8² + 8²) = √(64 + 64) = √128 = 8√2 inches.
Now, we substitute the diagonal into our radius formula:
Radius = (8√2) / 2 = 4√2 inches.
To express this in decimal form, we can approximate √2 (which is about 1.414):
Radius ≈ 4 * 1.414 = 5.656 inches.
Therefore, the radius of the circle in which the inscribed square has a side of 8 inches is 4√2 inches or approximately 5.656 inches.