1. **State the problem:** Calculate the cross-sectional area and volume of a cylinder with radius $r=15$ cm and height $h=27$ cm. 2. **Formula for cross-sectional area:** The cross-sectional area of a cylinder is the area of its circular base, given by the formula: $$A = \pi r^2$$ where $r$ is the radius. 3. **Calculate the cross-sectional area:** $$A = \pi \times 15^2 = \pi \times 225 = 225\pi$$ Using $\pi \approx 3.1416$: $$A \approx 225 \times 3.1416 = 706.858$$ Rounded to 1 decimal place: $$A \approx 706.9\ \text{cm}^2$$ 4. **Formula for volume:** The volume of a cylinder is given by: $$V = A \times h = \pi r^2 h$$ 5. **Calculate the volume:** $$V = \pi \times 15^2 \times 27 = \pi \times 225 \times 27 = 6075\pi$$ Using $\pi \approx 3.1416$: $$V \approx 6075 \times 3.1416 = 19084.5$$ Rounded to 1 decimal place: $$V \approx 19084.5\ \text{cm}^3$$