Question

Lateral surface of a cylinder with height of 12 and diameter of 14, 3.14 for pi

Answer 1

The lateral surface area \( A \) of a cylinder can be calculated using 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.

Given:
- Height \( h = 12 \)
- Diameter \( d = 14 \), hence the radius \( r = \frac{d}{2} = \frac{14}{2} = 7 \)

Now plug in the values into the formula:

\[
A = 2 \times 3.14 \times 7 \times 12
\]

Calculating step-by-step:

1. Calculate \( 2 \times 3.14 = 6.28 \)
2. Multiply this by the radius \( 7 \):

\[
6.28 \times 7 = 43.96
\]

3. Now multiply this result by the height \( 12 \):

\[
43.96 \times 12 = 527.52
\]

Thus, the lateral surface area of the cylinder is approximately:

\[
\text{Lateral Surface Area} \approx 527.52
\]

So the lateral surface area of the cylinder is \( 527.52 \) square units.