1. **State the problem:** We need to find the volume of a cylindrical grain silo with diameter 14 ft and height 38 ft. 2. **Formula for volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the radius:** The radius $r$ is half the diameter: $$r = \frac{14}{2} = 7 \text{ ft}$$ 4. **Substitute values into the formula:** $$V = 3.14 \times 7^2 \times 38$$ 5. **Calculate the square of the radius:** $$7^2 = 49$$ 6. **Calculate the volume:** $$V = 3.14 \times 49 \times 38$$ 7. **Multiply step-by-step:** $$3.14 \times 49 = 153.86$$ $$153.86 \times 38 = 5845.68$$ 8. **Round to the nearest whole number:** $$V \approx 5846 \text{ cubic feet}$$ **Final answer:** The volume of the silo is approximately **5846 ft³**.