1. The problem asks for the ratio of the area of the larger circle to the area of the smaller circle. 2. Recall the formula for the area of a circle: $$A = \pi r^2$$ where $r$ is the radius. 3. The larger circle has radius $r_1 = 2$ inches, so its area is $$A_1 = \pi (2)^2 = 4\pi$$. 4. The smaller circle has radius $r_2 = 1$ inch, so its area is $$A_2 = \pi (1)^2 = \pi$$. 5. The ratio of the areas is $$\frac{A_1}{A_2} = \frac{4\pi}{\pi}$$. 6. Canceling $\pi$ from numerator and denominator gives $$\frac{\cancel{\pi}4}{\cancel{\pi}} = 4$$. 7. Writing this as a ratio of whole numbers separated by a colon, we get $$4:1$$. Therefore, the ratio of the area of the larger circle to the area of the smaller circle is 4:1.