Final answer:
The area of a circle with a circumference of 8 inches is found by first finding the radius using the formula C = 2πr and then substituting into A = πr². The area, in terms of π, is 16 square inches.
Step-by-step explanation:
To find the area of a circle in terms of π (pi) when given the circumference, we can use the formula for the circumference of a circle, C = 2πr, where C is the circumference and r is the radius. The circumference is provided as 8 inches, so we have 8 = 2πr. Dividing both sides by 2π gives us r = 4/π inches.
Next, we use the formula for the area of a circle, A = πr², substituting the value of r we found from the circumference. Thus, we have A = π(4/π)². Simplifying this gives us A = (16/π)π = 16 square inches. Therefore, the area of the circle in terms of π is 16 square inches.