Question

formula for circumference:
$c=\pi r$
$c=\pi d^{2}$
$c=\pi r^{2}$
$c=2\pi r$

Explanation:

Step1: Recall circumference formula

The correct formula for the circumference of a circle relates the radius $r$ to the circumference $C$ as $C=2\pi r$, where $\pi$ is a constant approximately equal to 3.1416.

Step2: Eliminate incorrect options

• $C=\pi r$ is missing the factor of 2, so it is wrong.
• $C=\pi d^2$ and $C=\pi r^2$ are formulas for the area of a circle (with $d$ as diameter, $d=2r$), not circumference.

Answer:

$C=2\pi r$ (the formula in the red box)