1. **State the problem:** We need to find the area of the base and the volume of two cylinders. 2. **Formula for the area of the base of a cylinder:** The base is a circle, so its area is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Formula for the volume of a cylinder:** The volume is the area of the base times the height, $$V = A \times h = \pi r^2 h$$ where $h$ is the height. --- ### Cylinder a: - Radius $r = 5$ cm - Height $h = 10$ cm 4. Calculate the base area: $$A = \pi (5)^2 = 25\pi$$ 5. Calculate the volume: $$V = 25\pi \times 10 = 250\pi$$ 6. Approximate using $\pi \approx 3.14$: - Base area $\approx 25 \times 3.14 = 78.5$ cm$^2$ - Volume $\approx 250 \times 3.14 = 785$ cm$^3$ --- ### Cylinder b: - Radius $r = 3.4$ cm - Height $h = 9$ cm 7. Calculate the base area: $$A = \pi (3.4)^2 = \pi \times 11.56 = 11.56\pi$$ 8. Calculate the volume: $$V = 11.56\pi \times 9 = 104.04\pi$$ 9. Approximate using $\pi \approx 3.14$: - Base area $\approx 11.56 \times 3.14 = 36.29$ cm$^2$ - Volume $\approx 104.04 \times 3.14 = 326.78$ cm$^3$ --- **Final answers:** - Cylinder a base area: $78.5$ cm$^2$ - Cylinder a volume: $785$ cm$^3$ - Cylinder b base area: $36.29$ cm$^2$ - Cylinder b volume: $326.78$ cm$^3$