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 (\( r \)) = 25 inches
- Height (\( h \)) = 40 inches
Now, we can plug in the values:
- Calculate the area of the two circular bases:
\[ 2\pi r^2 = 2\pi (25^2) = 2\pi (625) = 1250\pi \]
- Calculate the area of the side (the lateral surface area):
\[ 2\pi rh = 2\pi (25)(40) = 2000\pi \]
- Add these two areas together:
\[ \text{Total Surface Area} = 1250\pi + 2000\pi = 3250\pi \]
Now, we round this to the nearest whole number after calculating \( 3250\pi \):
Using \( \pi \approx 3.14 \):
\[ 3250 \cdot 3.14 \approx 10295 \]
Now, rounding to the nearest whole number gives \( 10295 \).
Among the answer choices provided, the closest is 10210.
Thus, the final answer is:
10210.