Question

The lateral surface area of a cylinder with a height of 12 meters and a diameter of 14 meters is Response area.



Remember to use the π
symbol on your Desmos calculator.

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 that the diameter of the cylinder is 14 meters, the radius \( r \) is half of that:

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

The height \( h \) is given as 12 meters. Now, substituting these values into the formula:

\[
A = 2 \pi (7) (12)
\]

Calculating this step-by-step:

1. Calculate \( 7 \times 12 = 84 \).
2. Then multiply by \( 2 \): \( 2 \times 84 = 168 \).
3. Finally, include \( \pi \):

\[
A = 168 \pi \text{ square meters}
\]

So, the lateral surface area of the cylinder is:

\[
168 \pi \text{ square meters}
\]

If you want to calculate the numerical value, you can use \( \pi \approx 3.14 \) or type "168π" into your Desmos calculator for an exact result.