Question

Find the surface area of a cylinder that has a height of 12 m and a diameter of 130 cm. Use 3.14
for π
. Round to the nearest hundredth at the last step. (1 point)
_m^2

Answer 1

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

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

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

First, we need to convert the diameter of the cylinder to the radius. The diameter is given as 130 cm, so the radius \( r \) is:

\[
r = \frac{\text{diameter}}{2} = \frac{130 \text{ cm}}{2} = 65 \text{ cm}
\]

Next, we convert the radius into meters for our calculations. Since there are 100 cm in a meter:

\[
r = 65 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = 0.65 \text{ m}
\]

Now, we have:
- Height \( h = 12 \text{ m} \)
- Radius \( r = 0.65 \text{ m} \)

Substituting \( r \) and \( h \) into the surface area formula:

\[
\text{Surface Area} = 2 \cdot 3.14 \cdot 0.65 \cdot (12 + 0.65)
\]

Calculating \( (12 + 0.65) \):

\[
12 + 0.65 = 12.65
\]

Now substituting this back into the surface area formula:

\[
\text{Surface Area} = 2 \cdot 3.14 \cdot 0.65 \cdot 12.65
\]

Calculating step-by-step:

1. \( 2 \cdot 3.14 = 6.28 \)
2. \( 6.28 \cdot 0.65 \approx 4.077 \)
3. \( 4.077 \cdot 12.65 \approx 51.66305 \)

Finally, rounding to the nearest hundredth:

\[
\text{Surface Area} \approx 51.66 \text{ m}^2
\]

Thus, the surface area of the cylinder is:

\[
\boxed{51.66 \text{ m}^2}
\]