Cylinder Surface Area 2D90F4

1. **State the problem:** We need to find the total surface area of a cylindrical can with radius $r=8\text{ cm}$ and height $h=20\text{ cm}$. 2. **Formula for total surface area of a cylinder:** $$\text{Total Surface Area} = 2\pi r^2 + 2\pi r h$$ This formula includes the areas of the two circular bases ($2\pi r^2$) and the curved surface area ($2\pi r h$). 3. **Calculate the area of the two bases:** $$2\pi r^2 = 2 \times \pi \times 8^2 = 2 \times \pi \times 64 = 128\pi$$ 4. **Calculate the curved surface area:** $$2\pi r h = 2 \times \pi \times 8 \times 20 = 320\pi$$ 5. **Add both areas to get total surface area:** $$\text{Total Surface Area} = 128\pi + 320\pi = 448\pi$$ 6. **Approximate using $\pi \approx 3.1416$:** $$448 \times 3.1416 \approx 1407.44\text{ cm}^2$$ **Final answer:** The total surface area of the can is approximately $1407.44\text{ cm}^2$.