To find the surface area of the outside of a cylinder, we need to calculate the lateral surface area (the area around the sides) and the area of the two circular bases (top and bottom).
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Calculate the lateral surface area (A_l): The formula for the lateral surface area of a cylinder is:
\[ A_l = 2 \pi r h \]
where:
- \( r \) is the radius
- \( h \) is the height
Given:
- \( r = 4 \) feet
- \( h = 3 \) feet
Plugging in the values:
\[ A_l = 2 \times 3.14 \times 4 \times 3 \]
First, calculate \( 2 \times 3.14 \):
\[ 2 \times 3.14 = 6.28 \]
Now, compute:
\[ 6.28 \times 4 = 25.12 \]
Finally:
\[ 25.12 \times 3 = 75.36 \text{ square feet} \]
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Calculate the area of the top and bottom faces (A_b): The area of one circular base is given by:
\[ A_b = \pi r^2 \]
Since there are two bases, we multiply this area by 2:
\[ A_b = 2 \times \pi r^2 = 2 \times 3.14 \times (4)^2 \]
First, calculate \( (4)^2 \):
\[ (4)^2 = 16 \]
Now calculate:
\[ A_b = 2 \times 3.14 \times 16 \]
Compute \( 2 \times 3.14 \):
\[ 2 \times 3.14 = 6.28 \]
Now, find:
\[ 6.28 \times 16 = 100.48 \text{ square feet} \]
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Add the lateral surface area and the area of the bases to find the total surface area (A_total):
\[ A_{total} = A_l + A_b \]
Now, add:
\[ A_{total} = 75.36 + 100.48 = 175.84 \text{ square feet} \]
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Round to the nearest tenth:
The total surface area rounded to the nearest tenth is:
\[ \boxed{175.8} \text{ square feet} \]
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