To find the lateral surface area of a cylinder, you can use the formula:
\[ \text{Lateral Surface Area} = 2\pi rh \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given a diameter of 14 meters, the radius \( r \) is half of the diameter:
\[ r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ meters} \]
The height \( h \) is given as 12 meters. Now, substituting the values into the formula:
\[ \text{Lateral Surface Area} = 2\pi (7)(12) \]
Calculating this step by step:
- Calculate \( 2 \times 7 = 14 \).
- Then, \( 14 \times 12 = 168 \).
- Finally, multiply by \( \pi \):
\[ \text{Lateral Surface Area} = 168\pi \]
To get a numerical value, you can use the approximation \( \pi \approx 3.14 \):
\[ \text{Lateral Surface Area} \approx 168 \times 3.14 \approx 526.92 \text{ square meters} \]
Thus, the lateral surface area of the cylinder is:
\[ \text{Lateral Surface Area} \approx 168\pi \text{ square meters} \quad \text{(or approximately 526.92 square meters)} \]