To find the total surface area of a cylinder, we need to consider both the areas of the two circular bases and the lateral surface area (the area around the side of the cylinder).
Given:
- Height ([tex]\( h \)[/tex]) of the cylinder = 8 meters
- Radius ([tex]\( r \)[/tex]) of the base = 4 meters
- [tex]\( \pi \approx 3.14 \)[/tex]
### Step 1: Calculate the area of the two circular bases:
The area [tex]\( A \)[/tex] of a circle is given by the formula:
[tex]\[ A = \pi r^2 \][/tex]
We need to calculate this for one base and then multiply by 2 because there are two bases.
[tex]\[ A_{\text{base}} = \pi r^2 = 3.14 \times 4^2 \][/tex]
[tex]\[ A_{\text{base}} = 3.14 \times 16 \][/tex]
[tex]\[ A_{\text{base}} = 50.24 \, \text{m}^2 \][/tex]
Thus, for two bases:
[tex]\[ A_{\text{bases}} = 2 \times 50.24 = 100.48 \, \text{m}^2 \][/tex]
### Step 2: Calculate the lateral surface area:
The lateral surface area [tex]\( A_{\text{lateral}} \)[/tex] of a cylinder is given by the formula:
[tex]\[ A_{\text{lateral}} = 2 \pi r h \][/tex]
[tex]\[ A_{\text{lateral}} = 2 \times 3.14 \times 4 \times 8 \][/tex]
[tex]\[ A_{\text{lateral}} = 2 \times 3.14 \times 32 \][/tex]
[tex]\[ A_{\text{lateral}} = 6.28 \times 32 \][/tex]
[tex]\[ A_{\text{lateral}} = 200.96 \, \text{m}^2 \][/tex]
### Step 3: Calculate the total surface area:
The total surface area [tex]\( A_{\text{total}} \)[/tex] is the sum of the areas of the two bases and the lateral surface area.
[tex]\[ A_{\text{total}} = A_{\text{bases}} + A_{\text{lateral}} \][/tex]
[tex]\[ A_{\text{total}} = 100.48 + 200.96 \][/tex]
[tex]\[ A_{\text{total}} = 301.44 \, \text{m}^2 \][/tex]
So, the total surface area of the cylinder is [tex]\( 301.44 \, \text{m}^2 \)[/tex].
