To find the surface area of a cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Given:
- \( r = 5 \) cm,
- \( h = 15 \) cm.
Let's calculate the surface area step-by-step.
-
Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2\pi (5)^2 = 2\pi (25) = 50\pi \]
-
Calculate \( 2\pi rh \): \[ 2\pi rh = 2\pi (5)(15) = 2\pi (75) = 150\pi \]
-
Add both components together: \[ \text{Surface Area} = 50\pi + 150\pi = 200\pi \]
Now, we approximate \( \pi \) as 3.14: \[ 200\pi \approx 200 \times 3.14 = 628 \]
Therefore, the surface area of the cylinder is approximately:
\[ \boxed{628} \text{ square centimeters} \]
So the correct answer is 628 square centimeters.