To find the amount of fabric needed to reupholster the entire cushion, we need to calculate the surface area of the cylinder. The formula for the surface area \(A\) of a cylinder is given by:
\[ A = 2\pi r h + 2\pi r^2 \]
where \(r\) is the radius, \(h\) is the height, and \(\pi\) is approximately 3.14.
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Find the radius:
- The diameter of the cushion is 4 feet, therefore the radius \(r\) is: \[ r = \frac{diameter}{2} = \frac{4}{2} = 2 \text{ feet} \]
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Height:
- The height \(h\) is given as 1 foot.
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Calculate the surface area:
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First, calculate the lateral surface area (\(2\pi rh\)): \[ 2\pi rh = 2 \times 3.14 \times 2 \times 1 = 12.56 \text{ square feet} \]
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Next, calculate the area of the top and bottom circles (\(2\pi r^2\)): \[ 2\pi r^2 = 2 \times 3.14 \times (2^2) = 2 \times 3.14 \times 4 = 25.12 \text{ square feet} \]
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Total surface area: \[ A = 12.56 + 25.12 = 37.68 \text{ square feet} \]
So, the total amount of fabric needed to reupholster the entire cushion is 37.68 square feet.
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