1. The problem states that a right circular cylinder has a radius $r$ inches and height $h$ inches, and its volume is given as 10 cubic inches. 2. The formula for the volume $V$ of a right circular cylinder is: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. According to the problem, the volume $V$ is 10 cubic inches, so: $$\pi r^2 h = 10$$ 4. Since the problem asks for the volume of the cylinder and it is already given as 10 cubic inches, the volume is: $$\boxed{10}$$ 5. Therefore, the correct answer is option A: 10 cubic inches.