To find the amount of fabric needed to reupholster the entire cushion, we need to calculate the surface area of the cylinder-shaped cushion.
The formula for the surface area \( A \) of a cylinder is:
\[ A = 2\pi r(h + r) \]
Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- Diameter = 4 feet, thus the radius \( r = \frac{4}{2} = 2 \) feet,
- Height \( h = 1 \) foot.
Substituting the values into the formula:
\[ A = 2 \cdot 3.14 \cdot 2 \cdot (1 + 2) \] \[ A = 2 \cdot 3.14 \cdot 2 \cdot 3 \] \[ A = 2 \cdot 3.14 \cdot 6 \] \[ A = 12 \cdot 3.14 \] \[ A = 37.68 \text{ square feet} \]
Therefore, the amount of fabric needed to reupholster the entire cushion is 37.68 square feet.
So, the correct response is:
37.68 square feet.
1 answer