Question

The circumference of a circle is $88\text{cm}$. Its diameter is:

• A. $28\text{cm}$
• B. $42\text{cm}$
• C. $56\text{cm}$
• D. none of these

Answer 1

The correct option is A

$28\text{cm}$

Step 1: Finding the radius of circle

We know that, the circumference $C$ of the circle with radius $r$ is given by $C=2\mathrm{\pi r}$.

Given that, circumference $C$of circle $=88cm$

Substitute $C=88cm$ and use $\mathrm{\pi }=\frac{22}{7}$ into the formula $C=2\mathrm{\pi r}$.

$$\begin{gathered} \Rightarrow 88=2\times \frac{22}{7}\times r \\ \Rightarrow \frac{88}{2}\times \frac{7}{22}=r \\ \Rightarrow r=44\times \frac{7}{22} \\ \Rightarrow r=2\times 7 \\ \Rightarrow r=14cm \end{gathered}$$

Step 2: Finding the diameter

The diameter $d$ of the circle with radius $r$ is given by $d=2r$.

$\begin{array}{rcl}d& =& 2\times 14\\ & =& 28\text{cm}\end{array}$

Hence, the correct option is A.