Question

The lateral surface area of a cylinder with a height of 12 meters and a diameter of 14 meters is
1. 307.88
2. 527.79
3.1055.58

Answer 1

To find the lateral surface area (LSA) of a cylinder, you can use the formula:

\[
\text{LSA} = 2\pi rh
\]

where \( r \) is the radius and \( h \) is the height of the cylinder.

1. **Calculate the radius**: The diameter is given as 14 meters, so the radius \( r \) is half of that:

\[
r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ meters}
\]

2. **Use the given height**: The height \( h \) is given as 12 meters.

3. **Substitute the values into the LSA formula**:

\[
\text{LSA} = 2\pi(7)(12)
\]

Calculating:

\[
\text{LSA} = 2 \times \pi \times 7 \times 12 = 168\pi
\]

4. **Approximate \(\pi\) as 3.14 for calculation**:

\[
\text{LSA} \approx 168 \times 3.14 \approx 526.32 \text{ square meters}
\]

When rounded, this value is closest to 527.79.

Therefore, the correct answer is **2. 527.79**.