Question

4.
A cylinder has a height of 12 feet and a diameter of 10 feet. Solve for the approximate lateral surface area of the cylinder. Round to the nearest whole number

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. First, find the radius by dividing the diameter by 2:
\[
r = \frac{\text{Diameter}}{2} = \frac{10 \text{ feet}}{2} = 5 \text{ feet}
\]

2. Now, plug the radius and the height into the formula:
\[
h = 12 \text{ feet}
\]
\[
\text{Lateral Surface Area} = 2\pi (5 \text{ feet}) (12 \text{ feet})
\]

3. Calculate the lateral surface area:
\[
\text{Lateral Surface Area} = 2 \pi (5) (12)
\]
\[
= 120\pi \text{ square feet}
\]

4. Use \( \pi \approx 3.14 \) for approximation:
\[
\text{Lateral Surface Area} \approx 120 \times 3.14 \approx 376.8 \text{ square feet}
\]

5. Rounding to the nearest whole number:
\[
\text{Lateral Surface Area} \approx 377 \text{ square feet}
\]

Therefore, the approximate lateral surface area of the cylinder is **377 square feet**.