1. **State the problem:** Find the total surface area of two stacked cylinders. 2. **Given data:** - Top cylinder radius $r_1 = 5.4$ cm, height $h_1 = 4.7$ cm - Bottom cylinder radius $r_2 = 8.9$ cm, height $h_2 = 7.8$ cm 3. **Formula for surface area of a cylinder:** $$SA = 2\pi r^2 + 2\pi r h$$ where $2\pi r^2$ is the area of the two circular bases and $2\pi r h$ is the lateral surface area. 4. **Important note:** Since the cylinders are stacked, the top base of the bottom cylinder and the bottom base of the top cylinder are not exposed, so we subtract one base area from the total. 5. **Calculate surface area of top cylinder:** $$SA_1 = 2\pi (5.4)^2 + 2\pi (5.4)(4.7)$$ 6. **Calculate surface area of bottom cylinder:** $$SA_2 = 2\pi (8.9)^2 + 2\pi (8.9)(7.8)$$ 7. **Subtract one base area (top base of bottom cylinder):** $$\text{Overlap base area} = \pi (5.4)^2$$ 8. **Total surface area:** $$SA = SA_1 + SA_2 - \pi (5.4)^2$$ 9. **Calculate each term:** $$2\pi (5.4)^2 = 2\pi (29.16) = 183.26$$ $$2\pi (5.4)(4.7) = 2\pi (25.38) = 159.44$$ $$SA_1 = 183.26 + 159.44 = 342.7$$ $$2\pi (8.9)^2 = 2\pi (79.21) = 497.59$$ $$2\pi (8.9)(7.8) = 2\pi (69.42) = 436.25$$ $$SA_2 = 497.59 + 436.25 = 933.84$$ $$\pi (5.4)^2 = \pi (29.16) = 91.63$$ 10. **Final total surface area:** $$SA = 342.7 + 933.84 - 91.63 = 1184.91 \text{ cm}^2$$ **Answer:** The total surface area of the stacked cylinders is approximately $1184.91$ cm$^2$.