Question

What is the surface area of this cylinder? The radius is 5.2 m and the height is 16.8 m Surface area = Atop + Abottom + Aside Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth. The surface area of the cylinder is about _____ square meters

Answer 1

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

\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}}
\]

Where:
- \( A_{\text{top}} \) and \( A_{\text{bottom}} \) are the areas of the top and bottom circles, and
- \( A_{\text{side}} \) is the lateral surface area of the cylinder.

1. **Calculate the area of the top and bottom circles**:
\[
A_{\text{top}} = A_{\text{bottom}} = \pi r^2
\]

Substituting the radius \( r = 5.2 \, \text{m} \):
\[
A_{\text{top}} = A_{\text{bottom}} = 3.14 \times (5.2 \, \text{m})^2
\]
\[
(5.2)^2 = 27.04
\]
\[
A_{\text{top}} = A_{\text{bottom}} = 3.14 \times 27.04 \approx 84.93 \, \text{m}^2
\]
Therefore,
\[
A_{\text{top}} + A_{\text{bottom}} = 2 \times 84.93 \approx 169.86 \, \text{m}^2
\]

2. **Calculate the lateral surface area**:
\[
A_{\text{side}} = 2\pi rh
\]
Substituting \( r = 5.2 \, \text{m} \) and \( h = 16.8 \, \text{m} \):
\[
A_{\text{side}} = 2 \times 3.14 \times 5.2 \times 16.8
\]
\[
2 \times 3.14 \times 5.2 \approx 32.70
\]
\[
A_{\text{side}} \approx 32.70 \times 16.8 \approx 548.76 \, \text{m}^2
\]

3. **Total surface area**:
\[
\text{Surface Area} = A_{\text{top}} + A_{\text{bottom}} + A_{\text{side}} \approx 169.86 + 548.76
\]
\[
\text{Surface Area} \approx 718.62 \, \text{m}^2
\]

Thus, rounding the answer to the nearest hundredth, the surface area of the cylinder is approximately:

\[
\boxed{718.62} \text{ square meters}
\]