To calculate the surface area of a cylinder, we can use the formula:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \]
Where:
- \(A_{\text{top}}\) and \(A_{\text{bottom}}\) are the areas of the top and bottom circles,
- \(A_{\text{side}}\) is the area of the side of the cylinder.
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Area of the top and bottom circles: The area \(A\) of a circle is given by the formula: \[ A = \pi r^2 \] Where \(r\) is the radius. The radius \(r\) is 5 inches.
So, the area of one circle is: \[ A = \pi (5)^2 = \pi \cdot 25 = 25\pi \]
Thus, the combined area of the top and bottom is: \[ A_{\text{top}} + A_{\text{bottom}} = 25\pi + 25\pi = 50\pi \]
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Area of the side: The area of the side (the lateral surface area) of the cylinder is given by the formula: \[ A_{\text{side}} = 2\pi rh \] Where \(h\) is the height of the cylinder (9 inches).
Substituting the values: \[ A_{\text{side}} = 2\pi (5)(9) = 90\pi \]
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Total Surface Area: Now we combine all the areas to find the total surface area: \[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 50\pi + 90\pi = 140\pi \]
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Calculating with \(\pi \approx 3.14\): Now we substitute the value of \(\pi\): \[ \text{Surface Area} \approx 140 \cdot 3.14 = 439.6 \]
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Rounding: Rounding \(439.6\) to the nearest hundredth, we get: \[ \text{Surface Area} \approx 439.60 \text{ square inches} \]
So, the surface area of the cylinder is about 439.60 square inches.