1. **State the problem:** Find the volume of a cylinder with radius $r=7$ cm and height $h=20$ cm. 2. **Formula:** The volume $V$ of a cylinder is given by $$V = Bh = \pi r^2 h$$ where $B$ is the area of the base, $B = \pi r^2$. 3. **Calculate the base area:** $$B = \pi (7)^2 = 49\pi$$ 4. **Calculate the volume:** $$V = 49\pi \times 20 = 980\pi$$ 5. **Approximate using $\pi \approx 3.14$:** $$V \approx 980 \times 3.14 = 3077.2\text{ cm}^3$$ 6. **Compare with options:** The closest option is c) 3,078.8 cm³. **Final answer:** $\boxed{3,078.8\text{ cm}^3}$