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A belt is wrapped tautly around two circular pulleys of radii 5 m and 1 m whose centres are 8 m apart (external/crossed-free configuration as drawn). Find the total length of belt needed.

1. 8*sqrt(3) + 28*pi/3
2. 8*sqrt(3) + 14*pi/3
3. 8*sqrt(3) + 10*pi
4. 16 + 6*pi

Correct answer: 8*sqrt(3) + 28*pi/3

Solution

With a crossed belt over radii 5 and 1 and centres 8 apart, the two tangents total 8*sqrt(3) and the wrap arcs add 28*pi/3.

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