Final answer:
The circumference of a circle with a radius of 13 inches, given the original circle with a radius of 4 inches has a circumference of 25.12 inches, is 81.64 inches.
Step-by-step explanation:
The circumference of a circle is directly proportional to its radius, which means that if the radius changes, the circumference changes in the same ratio. You mentioned that a circle with a radius of 4 inches has a circumference of 25.12 inches, so the constant of proportionality is the c in the formula C = c * r, where C is the circumference and r is the radius. We can calculate c using the given circumference and radius (25.12 in. / 4 in. = 6.28), and then use it to find the circumference of a circle with a radius of 13 inches. Hence, the circumference would be 6.28 * 13 in. = 81.64 inches.