Question

the diameter is 11.4
the lenght is 13.5
What is the surface area of this cylinder?
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

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

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

Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder

First, we need to find the radius. The radius \( r \) is half of the diameter:

\[
r = \frac{\text{diameter}}{2} = \frac{11.4}{2} = 5.7
\]

Now, we can use the given length (which we are considering as the height \( h \)):

\[
h = 13.5
\]

Now we can substitute \( r \) and \( h \) into the surface area formula:

\[
\text{Surface Area} = 2\pi (5.7)^2 + 2\pi (5.7)(13.5)
\]

Calculating \( (5.7)^2 \):

\[
(5.7)^2 = 32.49
\]

Now, substituting it back:

\[
\text{Surface Area} = 2\pi (32.49) + 2\pi (5.7)(13.5)
\]

Calculating the two parts:

1. **First part**:

\[
2\pi (32.49) \approx 2 \times 3.14 \times 32.49 \approx 6.28 \times 32.49 \approx 204.60
\]

2. **Second part**:

Calculating \( (5.7)(13.5) \):

\[
(5.7)(13.5) = 76.95
\]

Now, calculating the second part:

\[
2\pi (76.95) \approx 2 \times 3.14 \times 76.95 \approx 6.28 \times 76.95 \approx 483.54
\]

Now, we can add both parts together:

\[
\text{Surface Area} \approx 204.60 + 483.54 \approx 688.14
\]

Thus, the surface area of the cylinder is:

\[
\boxed{688.14}
\]