To find the surface area of a cylinder, you can use the following formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
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Find the radius: The diameter of the cylinder is 12 inches, so the radius \( r \) is half of the diameter: \[ r = \frac{12}{2} = 6 , \text{inches} \]
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Substitute the values into the formula: Given \( r = 6 \) inches and \( h = 10 \) inches, using \( \pi \approx 3.14 \): \[ \text{Surface Area} = 2(3.14)(6^2) + 2(3.14)(6)(10) \]
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Calculate each part:
- The area of the two circular bases: \[ 2\pi r^2 = 2(3.14)(6^2) = 2(3.14)(36) = 2(113.04) = 226.08 , \text{in}^2 \]
- The area of the side (lateral surface area): \[ 2\pi rh = 2(3.14)(6)(10) = 2(3.14)(60) = 2(188.4) = 376.8 , \text{in}^2 \]
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Add both areas together: \[ \text{Surface Area} = 226.08 + 376.8 = 602.88 , \text{in}^2 \]
Thus, the surface area of the cylinder is approximately:
\[ \boxed{602.88} , \text{in}^2 \]