To calculate the surface area of the cylinder-shaped ottoman cushion, we use the formula for the surface area of a cylinder:
\[ SA = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is approximately 3.14.
Given:
- \( r = 3.5 \) feet,
- \( h = 2 \) feet.
Let's calculate the surface area step by step.
-
Calculate the area of the top and bottom circles (\(2\pi r^2\)): \[ 2\pi r^2 = 2 \cdot 3.14 \cdot (3.5)^2 \] \[ = 2 \cdot 3.14 \cdot 12.25 = 2 \cdot 3.14 \cdot 12.25 \approx 76.93 \text{ ft}^2 \]
-
Calculate the area of the side (\(2\pi rh\)): \[ 2\pi rh = 2 \cdot 3.14 \cdot 3.5 \cdot 2 \] \[ = 2 \cdot 3.14 \cdot 7 = 2 \cdot 21.98 \approx 43.96 \text{ ft}^2 \]
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Now, sum them up to find the total surface area: \[ SA = 76.93 + 43.96 \approx 120.89 \text{ ft}^2 \]
Thus, the total amount of fabric needed to cover the entire cushion of the ottoman is approximately:
\[ \boxed{120.89} \text{ ft}^2 \]