Question

What is the approximate surface area of the cylinder? Round your answer to the nearest tenth.
Hight is 20 in
radius 22 in

Answer 1

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

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

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

Given:
- Height \( h = 20 \) inches
- Radius \( r = 22 \) inches

Now, substituting these values into the formula:

1. Calculate the lateral surface area (the area of the side):
\[
\text{Lateral Surface Area} = 2\pi r h = 2\pi (22)(20) = 880\pi
\]

2. Calculate the area of the two circular bases:
\[
\text{Area of Bases} = 2\pi r^2 = 2\pi (22^2) = 2\pi (484) = 968\pi
\]

3. Combine the two areas:
\[
\text{Total Surface Area} = 880\pi + 968\pi = 1848\pi
\]

4. Approximating \( \pi \) as 3.14:
\[
\text{Total Surface Area} \approx 1848 \times 3.14 \approx 5784.72
\]

Therefore, rounding to the nearest tenth, the approximate surface area of the cylinder is:

\[
\text{Surface Area} \approx 5784.7 \text{ square inches}
\]