To find the surface area that needs to be refinished, we need to calculate the lateral surface area of the cylinder. The formula for the lateral surface area \( A \) of a cylinder is given by:
\[ A = 2\pi rh \]
where \( r \) is the radius and \( h \) is the height. In this case, the radius \( r \) is 4 feet and the height \( h \) is 30 feet.
Plugging in the values:
\[ A = 2 \times 3.14 \times 4 \times 30 \]
Calculating step-by-step:
- Calculate \( 2 \times 3.14 = 6.28 \).
- Calculate \( 6.28 \times 4 = 25.12 \).
- Calculate \( 25.12 \times 30 = 753.6 \).
Thus, the lateral surface area of the silo is:
\[ A = 753.6 \text{ square feet} \]
Rounding to the nearest tenth, the farmer needs:
\[ \boxed{753.6} \text{ square feet of aluminum to refinish the silo.} \]