To find the total surface area of a cylinder, you can use the formula:
\[ \text{Total Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius,
- \( h \) is the height.
Given:
- Height \( h = 15 \) feet,
- Radius \( r = 4 \) feet,
- Using \( \pi \approx 3.14 \).
Now, calculate each part of the formula step-by-step.
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Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4^2) = 2 \times 3.14 \times 16 = 100.48 \text{ feet}^2 \]
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Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 15 = 2 \times 3.14 \times 60 = 376.8 \text{ feet}^2 \]
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Add both areas to get the total surface area: \[ \text{Total Surface Area} = 100.48 + 376.8 = 477.28 \text{ feet}^2 \]
Now, round to the nearest tenth: \[ \text{Total Surface Area} \approx 477.3 \text{ feet}^2 \]
Therefore, the total surface area of the cylinder is 477.3 feet².
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