If you walk once around a circular park, the total distance you cover is like stretching the circular boundary into a straight line, which is $\pi$ times the diameter of that park.

In uniform circular motion, speed is defined as $v = \frac{d_{\text{total}}}{t}$. The distance covered in one revolution is the circumference $C = 2 \times \pi \times r$. Since the diameter $d = 2 \times r$, the circumference can be expressed as $C = \pi \times d$. Dividing this by the time $t$ gives $v = \frac{\pi \times d}{t}$.

Always verify if the formula uses radius or diameter. If diameter is given, use $\pi d$; if radius is given, use $2\pi r$.