1. **State the problem:** We need to find the volume of a cylinder with radius $r = 5.3$ inches and height $h = 8.4$ inches. 2. **Formula for volume of a cylinder:** $$V = \pi r^2 h$$ where $V$ is volume, $r$ is radius, and $h$ is height. 3. **Substitute the given values:** $$V = 3.14 \times (5.3)^2 \times 8.4$$ 4. **Calculate the radius squared:** $$5.3^2 = 28.09$$ 5. **Multiply to find volume:** $$V = 3.14 \times 28.09 \times 8.4$$ 6. **Calculate intermediate multiplication:** $$3.14 \times 28.09 = 88.1526$$ 7. **Final multiplication:** $$V = 88.1526 \times 8.4 = 740.480$$ 8. **Round to two decimal places:** $$V \approx 740.48$$ **Answer:** The volume of the cylinder is approximately $740.48$ cubic inches.