To find the amount of fabric needed to reupholster the entire cushion, we need to calculate the surface area of a cylinder. The formula for the surface area \( A \) of a cylinder is:
\[ A = 2\pi r(h + r) \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Given:
- Height \( h = 1 \) foot,
- Diameter = 4 feet, thus the radius \( r = \frac{4}{2} = 2 \) feet.
Now, substituting the values:
\[ A = 2 \times 3.14 \times 2 \times (1 + 2) \]
Calculating \( (1 + 2) \):
\[ 1 + 2 = 3 \]
Now substituting this back into the area formula:
\[ A = 2 \times 3.14 \times 2 \times 3 \]
Calculating \( 2 \times 3 = 6 \):
\[ A = 2 \times 3.14 \times 6 \]
Now performing the multiplication:
\[ A = 2 \times 18.84 = 37.68 \]
So, the total surface area, and therefore the amount of fabric needed, is:
\[ \boxed{37.68} \text{ square feet} \]
Thus, the answer is 37.68 square feet.
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