A white cylindrical silo has a diameter of 30 feet and a height of 80 feet. A red stripe with a horizontal width of 3 feet is painted on the silo, as shown, making two complete revolutions around it. What is the area of the stripe in square feet?

[asy]
size(250);defaultpen(linewidth(0.8));
draw(ellipse(origin, 3, 1));
fill((3,0)--(3,2)--(-3,2)--(-3,0)--cycle, white);
draw((3,0)--(3,16)^^(-3,0)--(-3,16));
draw((0, 15)--(3, 12)^^(0, 16)--(3, 13));
filldraw(ellipse((0, 16), 3, 1), white, black);
draw((-3,11)--(3, 5)^^(-3,10)--(3, 4));
draw((-3,2)--(0,-1)^^(-3,1)--(-1,-0.89));
draw((0,-1)--(0,15), dashed);
draw((3,-2)--(3,-4)^^(-3,-2)--(-3,-4));
draw((-7,0)--(-5,0)^^(-7,16)--(-5,16));
draw((3,-3)--(-3,-3), Arrows(6));
draw((-6,0)--(-6,16), Arrows(6));
draw((-2,9)--(-1,9), Arrows(3));
label("$3$", (-1.375,9.05), dir(260), fontsize(7));
label("$A$", (0,15), N);
label("$B$", (0,-1), NE);
label("$30$", (0, -3), S);
label("$80$", (-6, 8), W);[/asy]

$ \textbf{(A)}\; 120\qquad
\textbf{(B)}\; 180\qquad
\textbf{(C)}\; 240\qquad
\textbf{(D)}\; 360\qquad
\textbf{(E)}\; 480$
1. **Determine the dimensions of the cylindrical silo:**
   - Diameter of the silo: \(30\) feet.
   - Radius of the silo: \( \frac{30}{2} = 15 \) feet.
   - Height of the silo: \(80\) feet.

2. **Calculate the circumference of the base of the cylinder:**
   \[
   \text{Circumference} = 2 \pi \times \text{radius} = 2 \pi \times 15 = 30 \pi \text{ feet}
   \]

3. **Unroll the cylindrical surface to form a rectangle:**
   - The height of the rectangle is the height of the cylinder: \(80\) feet.
   - The width of the rectangle is the circumference of the base: \(30 \pi\) feet.

4. **Determine the shape and dimensions of the stripe:**
   - The stripe makes two complete revolutions around the cylinder.
   - The horizontal width of the stripe is \(3\) feet.
   - When unrolled, the stripe forms a parallelogram on the rectangle with a base of \(3\) feet and a height of \(80\) feet.

5. **Calculate the area of the stripe:**
   - The area of a parallelogram is given by \( \text{Area} = \text{base} \times \text{height} \).
   \[
   \text{Area} = 3 \text{ feet} \times 80 \text{ feet} = 240 \text{ square feet}
   \]

\[
\boxed{240}
\]