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Exercise 305
A white cylindrical silo has diameter $40$ feet and height $100$ feet. A red stripe of horizontal width $5$ feet is painted on it, making three complete revolutions around the silo. What is the area of the stripe in square feet?
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Solution
  1. Cut the lateral surface along a vertical line and unroll it. Placing the three revolutions side by side (a strip of width $3\cdot40\pi$ and height $100$), the stripe becomes a single slanted parallelogram.
  2. The parallelogram has horizontal width (base) $5$ and height $100$, no matter how many times the stripe winds around.
  3. Its area is $5\cdot100=\boxed{500}$ square feet.
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