Question

The lateral surface area
of a cylinder with a
height of 12 meters and
a diameter of 14 meters
is
.
*Hint: Don't forget to use
your Desmos calculator
and STAAR Reference
Sheet to help!
Remember to use the
symbol on your Desmos
calculat

Answer 1

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

\[
\text{Lateral Surface Area} = 2 \pi r h
\]

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

1. **Calculate the radius**:

Given the diameter is 14 meters, the radius \( r \) is:
\[
r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ meters}
\]

2. **Use the height**:

Given the height \( h \) is 12 meters.

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

Now plug the values of \( r \) and \( h \) into the formula:
\[
\text{Lateral Surface Area} = 2 \pi (7)(12)
\]

4. **Calculate**:

\[
\text{Lateral Surface Area} = 2 \pi (84) = 168 \pi \text{ square meters}
\]

5. **Approximate using \(\pi \approx 3.14\)** for practical purposes:

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

Thus, the lateral surface area of the cylinder is \( 168 \pi \) square meters or approximately \( 526.32 \) square meters.