Discussion
A cycloid generated by a circle of 30 mm diameter has an arch of base length
Answer: A
Correct answer: 94.2 mm
One arch spans the circumference of the rolling circle, since the circle turns exactly once between cusps: \[ \pi d = \pi \times 30 = 94.2\ \mathrm{mm}. \] Using the radius instead gives 47.1 mm, and the factor of two is the commonest error in setting out a cycloid.
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