1. **State the problem:** Calculate the surface area of a cylinder with height $h=10$ cm and diameter $d=6$ cm. 2. **Formula for surface area of a cylinder:** $$\text{Surface Area} = 2\pi r^2 + 2\pi r h$$ where $r$ is the radius and $h$ is the height. 3. **Calculate the radius:** $$r = \frac{d}{2} = \frac{6}{2} = 3 \text{ cm}$$ 4. **Calculate the surface area:** $$\text{Surface Area} = 2\pi (3)^2 + 2\pi (3)(10)$$ $$= 2\pi (9) + 2\pi (30)$$ $$= 18\pi + 60\pi$$ $$= 78\pi$$ 5. **Final answer:** $$\text{Surface Area} = 78\pi \approx 245.04 \text{ cm}^2$$ This means the total surface area of the cylinder is approximately 245.04 square centimetres.