Circumference of Circle — Radius 7cm

Question

Find the circumference of a circle whose radius is 7 cm. Use π = 22/7.

Solution — Step by Step

Why This Works

The formula $C = 2\pi r$ comes from the definition of $\pi$ itself. By definition, $\pi$ is the ratio of a circle’s circumference to its diameter — so $\pi = C/d$. Since diameter $d = 2r$, rearranging gives us $C = \pi d = 2\pi r$.

The value $\frac{22}{7}$ is an approximation of $\pi$ (actual value ≈ 3.14159…). CBSE Class 6, 7, and 8 problems almost always say “use $\pi = \frac{22}{7}$” — and they pick radius values that are multiples of 7 precisely so the fraction cancels cleanly.

This is why $r = 7$ cm is the most common radius in textbook circumference problems. When you see $\pi = \frac{22}{7}$ and $r = 7$, the answer will always be a whole number.

Alternative Method

You can also use $C = \pi d$ directly, since diameter = 2r = 14 cm.

Same answer, and this form is slightly faster when the problem gives you the diameter directly instead of the radius.

Common Mistake

A quick sanity check: circumference must be greater than the diameter (14 cm). An answer of 22 cm passes that check, which is why this mistake slips through — but 44 cm is the correct answer.