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 top and bottom circles, and
- \( A_{\text{side}} \) is the lateral surface area of the cylinder.
-
Calculate the area of the top and bottom circles: \[ A_{\text{top}} = A_{\text{bottom}} = \pi r^2 \]
Substituting the radius \( r = 5.2 , \text{m} \): \[ A_{\text{top}} = A_{\text{bottom}} = 3.14 \times (5.2 , \text{m})^2 \] \[ (5.2)^2 = 27.04 \] \[ A_{\text{top}} = A_{\text{bottom}} = 3.14 \times 27.04 \approx 84.93 , \text{m}^2 \] Therefore, \[ A_{\text{top}} + A_{\text{bottom}} = 2 \times 84.93 \approx 169.86 , \text{m}^2 \]
-
Calculate the lateral surface area: \[ A_{\text{side}} = 2\pi rh \] Substituting \( r = 5.2 , \text{m} \) and \( h = 16.8 , \text{m} \): \[ A_{\text{side}} = 2 \times 3.14 \times 5.2 \times 16.8 \] \[ 2 \times 3.14 \times 5.2 \approx 32.70 \] \[ A_{\text{side}} \approx 32.70 \times 16.8 \approx 548.76 , \text{m}^2 \]
-
Total surface area: \[ \text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \approx 169.86 + 548.76 \] \[ \text{Surface Area} \approx 718.62 , \text{m}^2 \]
Thus, rounding the answer to the nearest hundredth, the surface area of the cylinder is approximately:
\[ \boxed{718.62} \text{ square meters} \]
1 answer