To find the surface area of the cylinder, we can use the formula you provided:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \]
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Calculate the area of the top and bottom circles (both are the same): The area \( A \) of a circle is given by:
\[ A = \pi r^2 \]
For the top and bottom of the cylinder, the radius \( r = 8.1 \) ft:
\[ A_{\text{top}} = A_{\text{bottom}} = \pi (8.1)^2 \]
Using \( \pi \approx 3.14 \):
\[ A_{\text{top}} = A_{\text{bottom}} = 3.14 \times (8.1)^2 = 3.14 \times 65.61 \approx 206.19 \text{ square feet} \]
Since there are two circles (top and bottom):
\[ 2 \times 206.19 \approx 412.38 \text{ square feet} \]
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Calculate the circumference of the top circle: The circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
For the cylinder, the radius \( r = 8.1 \) ft:
\[ C = 2 \pi (8.1) = 2 \times 3.14 \times 8.1 \approx 51.03 \text{ feet} \]
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Calculate the area of the curved surface (side area): The area of the side (curved surface) \( A_{\text{side}} \) of the cylinder is given by:
\[ A_{\text{side}} = C \times h \]
Where \( h = 13.6 \) ft:
\[ A_{\text{side}} = 51.03 \times 13.6 \approx 694.23 \text{ square feet} \]
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Add all areas to find the total surface area:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 412.38 + 694.23 \approx 1106.61 \text{ square feet} \]
- Rounding to the nearest hundredth:
The surface area of the cylinder is approximately 1106.61 square feet.