1. **State the problem:** We are given a solid cylinder with radius $r = 8$ cm and volume $V = 3892$ cm³. We need to find the height $h$ of the cylinder, correct to one decimal place. 2. **Formula for the volume of a cylinder:** $$V = \pi r^2 h$$ where $r$ is the radius and $h$ is the height. 3. **Substitute the known values:** $$3892 = \pi \times 8^2 \times h$$ 4. **Simplify the radius squared:** $$3892 = \pi \times 64 \times h$$ 5. **Isolate $h$ by dividing both sides by $\pi \times 64$:** $$h = \frac{3892}{\pi \times 64}$$ 6. **Show cancellation explicitly:** $$h = \frac{3892}{\cancel{\pi} \times \cancel{64}} \times \frac{1}{\cancel{\pi} \times \cancel{64}}$$ (Note: Here we only cancel the multiplication to isolate $h$, actual cancellation is division by the product.) 7. **Calculate the denominator:** $$\pi \times 64 \approx 3.1416 \times 64 = 201.0619$$ 8. **Calculate $h$:** $$h = \frac{3892}{201.0619} \approx 19.35$$ 9. **Round to one decimal place:** $$h \approx 19.4$$ **Final answer:** The height $h$ of the cylinder is approximately **19.4 cm**.