To find the amount of fabric needed to reupholster the cylinder-shaped cushion, we need to calculate the surface area of the cylinder. The formula for the surface area (SA) of a cylinder is:
\[ SA = 2\pi r^2 + 2\pi rh \]
where \( r \) is the radius and \( h \) is the height.
Given:
- The height \( h \) is 1 foot.
- The diameter is 4 feet, so the radius \( r \) is half of the diameter:
\[ r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2 \text{ feet} \]
Now we can plug the values into the formula:
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Calculate the area of the two circular bases: \[ 2\pi r^2 = 2\pi(2^2) = 2\pi(4) = 8\pi \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2\pi(2)(1) = 4\pi \]
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Add the areas together: \[ SA = 8\pi + 4\pi = 12\pi \]
Now we can calculate \( 12\pi \): \[ SA \approx 12 \times 3.14 = 37.68 \text{ square feet} \]
Therefore, the amount of fabric needed to reupholster the entire cushion is:
37.68 square feet