1. **State the problem:** We need to find the total surface area of a figure made of two stacked cylinders: a smaller top cylinder with height 3 cm and radius 5 cm, and a larger bottom cylinder with height 10 cm and radius 7 cm. 2. **Recall the formula for the surface area of a cylinder:** The total surface area (SA) of a single cylinder is given by: $$SA = 2\pi r^2 + 2\pi r h$$ where $r$ is the radius and $h$ is the height. - $2\pi r^2$ is the area of the two circular bases. - $2\pi r h$ is the lateral surface area. 3. **Important note:** Since the two cylinders are stacked, the top base of the bottom cylinder and the bottom base of the top cylinder are joined and not exposed. So, we do not count the area of the touching bases between the two cylinders. 4. **Calculate the surface area of the top cylinder:** - Radius $r_1 = 5$ cm - Height $h_1 = 3$ cm Top cylinder surface area includes: - Top base area: $\pi r_1^2 = \pi \times 5^2 = 25\pi$ - Lateral area: $2\pi r_1 h_1 = 2\pi \times 5 \times 3 = 30\pi$ - Bottom base is not exposed (touching the bottom cylinder), so exclude it. So, top cylinder surface area = $25\pi + 30\pi = 55\pi$ 5. **Calculate the surface area of the bottom cylinder:** - Radius $r_2 = 7$ cm - Height $h_2 = 10$ cm Bottom cylinder surface area includes: - Bottom base area: $\pi r_2^2 = \pi \times 7^2 = 49\pi$ - Lateral area: $2\pi r_2 h_2 = 2\pi \times 7 \times 10 = 140\pi$ - Top base is not exposed (touching the top cylinder), so exclude it. So, bottom cylinder surface area = $49\pi + 140\pi = 189\pi$ 6. **Add the surface areas of both cylinders:** $$SA_{total} = 55\pi + 189\pi = 244\pi$$ 7. **Calculate the numerical value:** $$244\pi \approx 244 \times 3.1416 = 766.99$$ 8. **Round to the nearest whole number:** $$767$$ square centimeters **Final answer:** The total surface area of the stacked cylinders is approximately **767** square centimeters.