To find the surface area of a cylinder, you 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 circular bases.
- \( A_{\text{side}} \) is the lateral surface area of the cylinder.
- Calculating the area of the top and bottom:
The area of a circle is given by the formula:
\[ A = \pi r^2 \]
For the top and bottom of the cylinder:
\[ A_{\text{top}} = A_{\text{bottom}} = \pi (7.9)^2 \approx 3.14 \times (7.9)^2 \]
First, calculate \( (7.9)^2 \):
\[ (7.9)^2 = 62.4641 \]
Now calculate \( A_{\text{top}} \) and \( A_{\text{bottom}} \):
\[ A_{\text{top}} \approx 3.14 \times 62.4641 \approx 196.54 , \text{m}^2 \]
So the area for both the top and bottom is:
\[ A_{\text{top}} + A_{\text{bottom}} = 196.54 + 196.54 = 393.08 , \text{m}^2 \]
- Calculating the lateral surface area:
The lateral surface area \( A_{\text{side}} \) of the cylinder is given by:
\[ A_{\text{side}} = 2\pi rh \]
Where \( r = 7.9 , \text{m} \) and \( h = 10 , \text{m} \):
\[ A_{\text{side}} = 2 \times 3.14 \times 7.9 \times 10 \]
Calculating \( 2 \times 3.14 \times 7.9 \times 10 \):
\[ A_{\text{side}} \approx 2 \times 3.14 \times 7.9 \times 10 \approx 497.78 , \text{m}^2 \]
- Total Surface Area:
Now, add all the areas together:
\[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \approx 393.08 + 497.78 \approx 890.86 , \text{m}^2 \]
Rounding to the nearest hundredth, the surface area of the cylinder is approximately:
\[ \boxed{890.86} , \text{square meters} \]
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