1. **State the problem:** We are given the radius $r=7$ cm and the volume $V=3846.5$ cm³ of a cylinder. We need to find the height $h$ of the cylinder. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ This formula states that the volume is equal to the area of the base (a circle with radius $r$) times the height $h$. 3. **Rearrange the formula to solve for height $h$:** $$h = \frac{V}{\pi r^2}$$ 4. **Substitute the known values:** $$h = \frac{3846.5}{\pi \times 7^2}$$ 5. **Calculate the denominator:** $$7^2 = 49$$ 6. **Substitute and simplify:** $$h = \frac{3846.5}{\pi \times 49}$$ 7. **Calculate $\pi \times 49$:** $$\pi \times 49 \approx 3.1416 \times 49 = 153.9384$$ 8. **Calculate the height:** $$h = \frac{3846.5}{153.9384} \approx 25$$ **Final answer:** The height of the cylinder is approximately $25$ cm.