1. **State the problem:** Calculate the volume of a cylinder with radius $r=15$ cm and height $h=27$ cm. 2. **Formula:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute the values:** $$V = \pi \times 15^2 \times 27$$ 4. **Calculate the square of the radius:** $$15^2 = 225$$ 5. **Multiply:** $$V = \pi \times 225 \times 27$$ 6. **Calculate the product inside:** $$225 \times 27 = 6075$$ 7. **So:** $$V = \pi \times 6075$$ 8. **Use $\pi \approx 3.1416$ to approximate:** $$V \approx 3.1416 \times 6075 = 19084.5$$ 9. **Round to 1 decimal place:** $$V \approx 19084.5 \text{ cm}^3$$ **Final answer:** The volume of the cylinder is approximately $19084.5$ cubic centimeters.