1. **State the problem:** We need to find which pair of radius and height values produces the greatest volume for a cylinder. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the volume for each pair:** - For $r=1$, $h=4$: $$V = \pi \times 1^2 \times 4 = 4\pi$$ - For $r=2$, $h=3$: $$V = \pi \times 2^2 \times 3 = 12\pi$$ - For $r=3$, $h=2$: $$V = \pi \times 3^2 \times 2 = 18\pi$$ - For $r=4$, $h=1$: $$V = \pi \times 4^2 \times 1 = 16\pi$$ 4. **Compare the volumes:** $$4\pi < 12\pi < 16\pi < 18\pi$$ 5. **Conclusion:** The greatest volume is $18\pi$ cubic feet, which occurs when the radius is 3 ft and the height is 2 ft.