1. **State the problem:** We need to find the volume of a cylinder with height $h = 40$ cm and diameter $d = 14$ cm. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Find the radius:** The radius $r$ is half the diameter: $$r = \frac{d}{2} = \frac{14}{2} = 7 \text{ cm}$$ 4. **Substitute values into the volume formula:** $$V = \pi \times 7^2 \times 40$$ 5. **Calculate the volume:** $$V = \pi \times 49 \times 40 = 1960\pi$$ 6. **Evaluate using $\pi \approx 3.1416$:** $$V \approx 1960 \times 3.1416 = 6157.52 \text{ cm}^3$$ 7. **Round to 1 decimal place:** $$V \approx 6157.5 \text{ cm}^3$$ **Final answer:** The volume of the cylinder is approximately $6157.5$ cubic centimeters.