Question

Circumference of a circle is always-

• A. more than three times of its diameter
• B. three times of its diameter
• C. less than three times of its diameter
• D. three times of its radius

Answer 1

The correct option is A

more than three times of its diameter

Step 1: Write the formula for circumference in terms of radius.

A distance covered by traveling once around a circle is its perimeter, usually called its circumference.

$\mathrm{circumference}=2\mathrm{\pi r}$.

Where, $r$ is the radius of the circle and $\pi$ is a constant $\left(\pi =\frac{22}{7}\right)$.

Step 2: Put $\pi =\frac{22}{7}$in above equation.

$$\begin{gathered} \mathrm{circumference}=2\times \frac{22}{7}\times r \\ =\frac{22}{7}\times \left(2r\right) \end{gathered}$$.

Know that the diameter of a circle is double of its radius:

Let $D$ is the diameter of the circle.

$\Rightarrow D=2r$

Therefore,

$$\begin{gathered} \mathrm{circumference}=\frac{22}{7}\times D \\ \Rightarrow \mathrm{circumference}=3.1416\times D \end{gathered}$$

Hence the circumference of a circle is always more than three times of its diameter.