Final answer:
The ratio of the green-painted area to the yellow-painted area is 8:1, calculated by dividing the area of the ring (green region) by the area of the smaller circle (yellow region), resulting in the correct answer being 'None of the above'.
Step-by-step explanation:
The question asks for the ratio of the green-painted area to the yellow-painted area between two concentric circles with diameters of 1 inch and 3 inches, respectively. We start by calculating the area of each circle. The area of a circle is given by πr2, where r is the radius. The radius of the smaller circle is 0.5 inches, and the radius of the larger circle is 1.5 inches.
The area of the yellow-painted circle (smaller circle) is π(0.5)2 = 0.25π square inches. The area of the larger circle is π(1.5)2 = 2.25π square inches. Now, to find the area that is painted green, we subtract the area of the smaller circle from the area of the larger circle: 2.25π - 0.25π = 2π square inches.
To determine the ratio of the green area to the yellow area, we divide the green area by the yellow area:
(2π) / (0.25π) = 8.
Hence, the ratio of the green-painted area to the yellow-painted area is 8:1, which is not listed in the given answer choices, so the correct answer is None of the above.