To find the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
Given:
- The diameter of the base is 8 inches, thus the radius \( r = \frac{8}{2} = 4 \) inches.
- The height \( h = 10 \) inches.
Now, substitute these into the formula:
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Calculate the area of the two bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 , \text{in}^2 \]
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Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 10 = 2 \times 3.14 \times 40 = 251.2 , \text{in}^2 \]
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Add the areas together to find the total surface area: \[ \text{Surface Area} = 100.48 + 251.2 = 351.68 , \text{in}^2 \]
Thus, the surface area of the cylinder is \( \boxed{351.68} , \text{in}^2 \).