The circumference is the distance around the outside of a circle (its perimeter).
$$C = \pi d = 2\pi r$$
where $d$ is the diameter and $r$ is the radius ($d = 2r$).
Example: Find the circumference of a circle with radius 5 cm. $$C = 2\pi \times 5 = 10\pi \approx 31.4\text{ cm}$$
Finding radius or diameter from circumference: rearrange. $$d = \frac{C}{\pi} \qquad r = \frac{C}{2\pi}$$
Example: A circle has circumference 40 cm. Find the diameter. $$d = \frac{40}{\pi} \approx 12.7\text{ cm}$$
Exact answers: leave in terms of $\pi$ when asked (e.g. $10\pi$ cm).
Perimeter of a semicircle = half the circumference + the diameter. $$P = \pi r + 2r$$
Common error: using diameter where radius is needed (or vice versa) — always check which one the question gives you.
Arcs & sectors Area of a circle
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Use the $\pi$ key throughout. Avoid rounding mid-calculation.