1. **State the problem:** Find the volume and surface area of a right circular cylinder with diameter 6 inches and height 12 inches. 2. **Formulas:** - Volume of cylinder: $$V = \pi r^2 h$$ - Surface area of cylinder: $$A = 2\pi r^2 + 2\pi r h$$ 3. **Calculate radius:** - Diameter $d = 6$ inches, so radius $r = \frac{d}{2} = \frac{6}{2} = 3$ inches. 4. **Calculate volume:** $$V = \pi (3)^2 (12) = \pi \times 9 \times 12 = 108\pi$$ cubic inches. 5. **Calculate surface area:** $$A = 2\pi (3)^2 + 2\pi (3)(12) = 2\pi \times 9 + 2\pi \times 36 = 18\pi + 72\pi = 90\pi$$ square inches. **Final answers:** - Volume = $108\pi$ cubic inches - Surface area = $90\pi$ square inches