To calculate the surface area of a cylinder, we use the following formula:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \]
Where:
- \( A_{\text{top}} = \pi r^2 \) (area of the top circle)
- \( A_{\text{bottom}} = \pi r^2 \) (area of the bottom circle)
- \( A_{\text{side}} = 2 \pi r h \) (area of the side)
Given:
- Radius \( r = 6 \) yd
- Height \( h = 11 \) yd
- Use \( \pi \approx 3.14 \)
Now, calculate each part:
-
Area of the top and bottom circles: \[ A_{\text{top}} = A_{\text{bottom}} = \pi r^2 = 3.14 \times (6^2) = 3.14 \times 36 = 113.04 , \text{square yards} \]
So, \[ A_{\text{top}} + A_{\text{bottom}} = 113.04 + 113.04 = 226.08 , \text{square yards} \]
-
Area of the side: \[ A_{\text{side}} = 2 \pi r h = 2 \times 3.14 \times 6 \times 11 \]
First, calculate \( 2 \times 6 = 12 \): \[ A_{\text{side}} = 12 \times 3.14 \times 11 \] Now calculate \( 3.14 \times 11 = 34.54 \): \[ A_{\text{side}} = 12 \times 34.54 = 414.48 , \text{square yards} \]
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Total Surface Area: \[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} = 226.08 + 414.48 = 640.56 , \text{square yards} \]
Finally, rounding to the nearest hundredth, the surface area of the cylinder is:
\[ \boxed{640.56} , \text{square yards} \]
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