To calculate the surface area of a cylinder, you need to find the lateral surface area and the area of the two circular bases. The total surface area (SA) of a cylinder is given by:
\[ SA = 2\pi r h + 2\pi r^2 \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given:
- Radius \( r = 4 \) feet
- Height \( h = 3 \) feet
- Using \( \pi \approx 3.14 \)
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Calculate the lateral surface area: \[ \text{Lateral Surface Area} = 2\pi rh = 2 \times 3.14 \times 4 \times 3 \] \[ = 2 \times 3.14 \times 12 = 2 \times 37.68 = 75.36 \text{ square feet} \]
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Calculate the area of the two circular bases: \[ \text{Area of one base} = \pi r^2 = 3.14 \times 4^2 = 3.14 \times 16 = 50.24 \text{ square feet} \] \[ \text{Area of two bases} = 2 \times 50.24 = 100.48 \text{ square feet} \]
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Now combine both areas to get the total surface area: \[ SA = \text{Lateral Surface Area} + \text{Area of two bases} = 75.36 + 100.48 = 175.84 \text{ square feet} \]
Finally, rounding to the nearest tenth, the surface area of the cylinder is: \[ \boxed{175.8} \text{ square feet} \]
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