Arcs From Degrees

When the angle comes in degrees, convert it first. A bicycle wheel of radius 20 cm turns through 72°. In radians that is $\frac{72\cdot \pi}{180}$, which is $\frac{2\pi}{5}$, so the arc is $s = \frac{20\cdot 2\pi}{5}$, which is $8\pi$ cm, about 25.13 cm.

The same answer comes from fractions of the circle. 72° is 72/360, a fifth, of a turn, so the arc is a fifth of the circumference $40\pi$: again $8\pi$. Both routes say the same thing; the formula just saves writing.

The trap is skipping the conversion: 20 × 72 = 1440 cm, more than eleven times the whole circumference.