To calculate the amount of fabric needed to reupholster the entire cylinder-shaped cushion, you need to find the surface area of the cylinder. The formula for the surface area \( A \) of a cylinder is:
\[ A = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
Given:
- Diameter of the cushion = 4 feet, therefore the radius \( r = \frac{4}{2} = 2 \) feet.
- Height \( h = 1 \) foot.
- Using \( \pi \approx 3.14 \).
Now, we can calculate the surface area.
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Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times (2)^2 = 2 \times 3.14 \times 4 = 25.12 \text{ square feet} \]
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Calculate \( 2\pi rh \): \[ 2\pi rh = 2 \times 3.14 \times 2 \times 1 = 2 \times 3.14 \times 2 = 12.56 \text{ square feet} \]
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Add the two areas together to get the total surface area: \[ A = 25.12 + 12.56 = 37.68 \text{ square feet} \]
Thus, the total fabric needed to reupholster the cushion is 37.68 square feet.
So, the correct response is:
37.68 square feet.
1 answer