1. **State the problem:** Whitney wants to find the surface area of a bird feeder made of two coaxial cylinders, one on top of the other. 2. **Identify the dimensions:** - Top cylinder diameter = 5 cm, so radius $r_1 = \frac{5}{2} = 2.5$ cm - Top cylinder height = 9 cm - Bottom cylinder diameter = 8 cm, so radius $r_2 = \frac{8}{2} = 4$ cm - Bottom cylinder height = 1.5 cm 3. **Formula for surface area of a cylinder:** $$\text{Surface Area} = 2\pi r h + 2\pi r^2$$ where $2\pi r h$ is the lateral surface area and $2\pi r^2$ is the area of the two circular bases. 4. **Important note:** Since the two cylinders are coaxial and stacked, the top base of the bottom cylinder is covered by the bottom of the top cylinder, so we do not count that base twice. 5. **Calculate lateral surface areas:** - Top cylinder lateral area: $$2\pi r_1 h_1 = 2\pi (2.5)(9) = 45\pi$$ - Bottom cylinder lateral area: $$2\pi r_2 h_2 = 2\pi (4)(1.5) = 12\pi$$ 6. **Calculate the exposed bases:** - Top cylinder top base area: $$\pi r_1^2 = \pi (2.5)^2 = 6.25\pi$$ - Bottom cylinder bottom base area: $$\pi r_2^2 = \pi (4)^2 = 16\pi$$ 7. **Sum all parts:** $$\text{Total Surface Area} = \text{top lateral} + \text{bottom lateral} + \text{top base} + \text{bottom base}$$ $$= 45\pi + 12\pi + 6.25\pi + 16\pi = (45 + 12 + 6.25 + 16)\pi = 79.25\pi$$ 8. **Calculate numerical value:** $$79.25 \times 3.1416 \approx 248.9$$ **Final answer:** The surface area of the bird feeder is approximately **248.9 square centimetres**.