Question

Circumference of a circle of diameter $5\mathrm{cm}$is-

• A. $3.14\mathrm{cm}$
• B. $31.4\mathrm{cm}$
• C. $15.7\mathrm{cm}$
• D. $1.57\mathrm{cm}$

Answer 1

The correct option is C

$15.7\mathrm{cm}$

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.

$$\begin{gathered} \mathrm{circumference}=2\pi r \\ =\pi \left(2r\right) \end{gathered}$$

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

Step 2: Apply the above relation and find the circle's radius.

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

Let $d$ is the diameter of the circle.

So, $d=2r$

Therefore,

$$\begin{gathered} \mathrm{circumference}=\pi d \\ \Rightarrow \mathrm{circumference}=\frac{22}{7}\times 5 \\ \Rightarrow \mathrm{circumference}=3.14\times 5 \\ \Rightarrow \mathrm{circumference}=15.7\mathrm{cm} \end{gathered}$$

Hence the correct option is (C).