Question

A lateral surface area of a cylinder with a height of 12 meters and a diameter of 14 meters is ___________________________

Answer 1

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

\[
A = 2 \pi r h
\]

where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.

First, you need to find the radius from the diameter:

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

Now, you can plug the radius and height into the formula:

\[
h = 12 \text{ meters}
\]
\[
A = 2 \pi (7) (12)
\]
\[
A = 2 \pi \times 7 \times 12 = 168 \pi
\]

Now, if you want to calculate the numerical value of \( A \):

\[
A \approx 168 \times 3.14159 \approx 526.79 \text{ square meters}
\]

Thus, the lateral surface area of the cylinder is approximately \( 526.79 \) square meters, or it can be expressed as \( 168\pi \) square meters.