To find the surface area that the farmer needs to refinish, we need to calculate the lateral surface area of the cylinder (silo). The formula for the lateral surface area \( A \) of a cylinder is given by:
\[ A = 2 \pi r h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- Radius \( r = 4 \) feet,
- Height \( h = 30 \) feet.
Now we plug in the values into the formula:
\[ A = 2 \times 3.14 \times 4 \times 30 \]
Calculating this step by step:
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Calculate \( 2 \times 3.14 \): \[ 2 \times 3.14 = 6.28 \]
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Next, calculate \( 6.28 \times 4 \): \[ 6.28 \times 4 = 25.12 \]
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Now, multiply \( 25.12 \) by \( 30 \): \[ 25.12 \times 30 = 753.6 \]
Thus, the lateral surface area of the silo is \( 753.6 \) square feet. Therefore, the farmer needs to refinish:
\[ \boxed{753.6} \]
square feet of aluminum.