Barber Pole

The revolving portion of a splendid barber pole is a cylinder 4 feet tall and 6 inches in radius. The red stripe is painted in a spiral around the cylinder and makes exactly 8 complete turns around it from bottom to top. How long is the stripe? (Ignore its width.)

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Unwind the stripe!

stripe2 = 3022 + 482 = 93508
stripe ≈ 306″, or about 25½ feet.

You can make a great model of this problem by drawing the right triangle with a red hypotenuse and wrapping it around a pencil (tape the 48 inch side to the pencil first). Unwrap it in front of the class when they’ve gotten stuck and watch their eyes widen.

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