Final answer:
The circumference of the circle is found to be 116π units, by first simplifying the given ratio of the area to the circumference and then substituting the calculated radius back into the circumference formula.
Step-by-step explanation:
The student is asked to find the circumference of a circle given the ratio of the area of the circle to its circumference is 29/1.
We start with the formula for the area of a circle, A = πr², and the formula for the circumference of a circle, C = 2πr. The ratio given is 29/1, meaning A/C = 29/1 = (πr²) / (2πr). Simplifying this ratio by canceling out π and r, we get r/2 = 29/1. Multiplying both sides by 2 gives r = 58. Now substituting this value back into the circumference formula, we obtain C = 2π(58) which simplifies to C = 116π. Therefore, the circumference of the circle is 116π units.