To find the surface area of a cylinder, we can use the following formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius
- \( h \) is the height
Given:
- \( r = 25 \) inches
- \( h = 40 \) inches
Now, substituting the values into the formula:
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Calculate the lateral surface area: \[ 2\pi rh = 2\pi (25)(40) = 2\pi (1000) = 2000\pi \]
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Calculate the area of the top and bottom surfaces: \[ 2\pi r^2 = 2\pi (25^2) = 2\pi (625) = 1250\pi \]
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Add the lateral surface area and the area of the top and bottom: \[ \text{Surface Area} = 2000\pi + 1250\pi = 3250\pi \]
Now, approximate \( \pi \) as \( 3.14 \) to find the numerical value: \[ \text{Surface Area} \approx 3250 \times 3.14 \approx 10295 \]
The closest option among your provided choices would be approximately \( 10,210 , \text{in}^2 \).
So, the surface area of the cylinder is approximately 10,210 in².