To find the amount of fabric needed to cover the entire cushion of the cylinder-shaped ottoman, we will calculate the surface area using the formula for the surface area of a cylinder:
\[ \text{SA} = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius
- \( h \) is the height
- \( \pi \) is approximately 3.14
Given:
- Radius \( r = 3.5 \) feet
- Height \( h = 2 \) feet
Let's calculate the surface area step by step.
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Calculate \( 2\pi r^2 \): \[ 2\pi r^2 = 2 \times 3.14 \times (3.5)^2 \] First, calculate \( (3.5)^2 \): \[ (3.5)^2 = 12.25 \] Now calculate \( 2 \times 3.14 \times 12.25 \): \[ 2 \times 3.14 \times 12.25 = 2 \times 3.14 \times 12.25 = 76.93 \]
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Calculate \( 2\pi rh \): \[ 2\pi rh = 2 \times 3.14 \times 3.5 \times 2 \] Calculate \( 3.5 \times 2 \): \[ 3.5 \times 2 = 7 \] Now calculate \( 2 \times 3.14 \times 7 \): \[ 2 \times 3.14 \times 7 = 43.96 \]
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Add the two areas together: \[ SA = 76.93 + 43.96 = 120.89 \]
So the total surface area of the cushion is 120.89 square feet.
Thus, the amount of fabric needed to cover the entire cushion of the ottoman is 120.89 ft².