What is the surface area of this cylinder? The radius is 7.9 m and the height is 10 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 calculate the surface area of the cylinder, we use the formula:

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

Where:

• \(A_{\text{top}} = \pi r^2\) (area of the top circle)
• \(A_{\text{bottom}} = \pi r^2\) (area of the bottom circle)
• \(A_{\text{side}} = 2\pi rh\) (surface area of the side)

Given:

• Radius \(r = 7.9,m\)
• Height \(h = 10,m\)
• Using \(\pi \approx 3.14\)

1. Calculate \(A_{\text{top}}\) and \(A_{\text{bottom}}\):

\[ A_{\text{top}} = \pi r^2 = 3.14 \times (7.9)^2 \] \[ = 3.14 \times 62.41 \approx 196.77,m^2 \]

Since \(A_{\text{top}} = A_{\text{bottom}}\), we have:

\[ A_{\text{bottom}} \approx 196.77,m^2 \]

2. Calculate \(A_{\text{side}}\):

\[ A_{\text{side}} = 2\pi rh = 2 \times 3.14 \times 7.9 \times 10 \] \[ = 2 \times 3.14 \times 79 \approx 497.46,m^2 \]

3. Adding all parts to find the total surface area:

\[ \text{Surface Area} \approx 196.77 + 196.77 + 497.46 \] \[ \approx 890.00,m^2 \]

Thus, the surface area of the cylinder is about 890.00 square meters.