Question

Keith has made a square that has 6-inch cord sides. He bends the square into a circular loop. What is the maximum radius of the circular loop? Round to the nearest tenth.

A. 3.0 inches
B. 3.4 inches
C. 3.8 inches
D. 4.2 inches

Answer 1

The maximum radius of the circular loop formed from a square with 6-inch sides is approximately 4.2 inches.

Step-by-step explanation:

To find the maximum radius of the circular loop formed from a square with 6-inch sides, we need to determine the diagonal of the square. The diagonal of a square can be found using the Pythagorean theorem: diagonal = side * sqrt(2). In this case, diagonal = 6 * sqrt(2). The radius of the circular loop is half the diagonal, so radius = diagonal / 2. Plugging in the value for the diagonal, we get: radius = (6 * sqrt(2)) / 2 = 3 * sqrt(2). Rounding to the nearest tenth gives us an approximate maximum radius of 4.2 inches (D).