To calculate the lateral surface area of a cylinder, you can use the formula:
\[ Lateral \ Surface \ Area = 2\pi rh \]
where \( r \) is the radius and \( h \) is the height.
Given:
- Height (\( h \)) = 12 meters
- Diameter = 14 meters, so the radius (\( r \)) = Diameter / 2 = 14 m / 2 = 7 meters.
Now, substitute the values into the formula:
\[ Lateral \ Surface \ Area = 2 \pi (7 , m) (12 , m) \]
Calculating this gives:
\[ Lateral \ Surface \ Area = 2 \pi (84 , m^2) = 168\pi , m^2 \]
Using an approximate value for \( \pi \approx 3.14 \):
\[ Lateral \ Surface \ Area \approx 168 \times 3.14 \approx 526.32 , m^2 \]
Now, if you use a more accurate value of \( \pi \) on your calculator (around 3.14159):
\[ Lateral \ Surface \ Area \approx 168 \times 3.14159 \approx 527.79 , m^2 \]
Based on the choices provided:
- 307.88 sq. meters
- 527.79 sq. meters
- 1055.58 sq. meters
The correct answer is 527.79 sq. meters.