1. **Problem:** Find the radius of a cone-shaped funnel that holds 314 cubic inches of water with a height of 12 inches. Use 3.14 for pi. 2. **Formula:** The volume of a cone is given by $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Step 1:** Substitute the known values into the formula: $$314 = \frac{1}{3} \times 3.14 \times r^2 \times 12$$ 4. **Step 2:** Simplify the right side: $$314 = \frac{1}{3} \times 3.14 \times 12 \times r^2 = 12.56 r^2$$ 5. **Step 3:** Solve for $r^2$ by dividing both sides by 12.56: $$r^2 = \frac{314}{12.56}$$ 6. **Step 4:** Show cancellation: $$r^2 = \frac{\cancel{314}}{\cancel{12.56}} = 25$$ 7. **Step 5:** Take the square root of both sides to find $r$: $$r = \sqrt{25} = 5$$ **Answer:** The radius of the funnel is 5 inches.