1. **State the problem:** We need to find the volume of a cylindrical tin with height $20$ cm and radius $8$ cm. 2. **Formula for the volume of a cylinder:** The volume $V$ of a cylinder is given by the formula: $$V = \pi r^2 h$$ where $r$ is the radius of the base and $h$ is the height. 3. **Substitute the given values:** Here, $r = 8$ cm and $h = 20$ cm, so: $$V = \pi \times 8^2 \times 20$$ 4. **Calculate the square of the radius:** $$8^2 = 64$$ 5. **Calculate the volume:** $$V = \pi \times 64 \times 20$$ 6. **Multiply the constants:** $$64 \times 20 = 1280$$ 7. **Final volume in terms of $\pi$:** $$V = 1280\pi \text{ cm}^3$$ **Answer:** The volume of the cylindrical tin is $1280\pi$ cubic centimeters.