To find the surface area of a cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Given:
- Radius \( r = 5 \) inches,
- Height \( h = 10 \) inches,
- \( \pi \approx 3.14 \).
Now, plug the values into the formula.
-
Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (5^2) = 2 \times 3.14 \times 25 = 157 , \text{square inches}. \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 5 \times 10 = 2 \times 3.14 \times 50 = 314 , \text{square inches}. \]
-
Add both areas together to find the total surface area: \[ \text{Surface Area} = 157 + 314 = 471 , \text{square inches}. \]
So, the surface area of the cylinder is \( \boxed{471} \) square inches.