Question

If the circumference of a circle is $176\text{ cm}$, find its radius.

Answer 1

Hint: To solve this question we use the formula of circumference of a circle which is given by $2\pi r$, where $r$ is radius of a circle. As given in the question the circumference of a circle is $176\text{ cm}$, so equating this value to the $2\pi r$ and substitute the value $\pi ={\displaystyle \frac{22}{7}}$ we obtain the value of radius of a circle.

Complete step-by-step answer:
We have given that the circumference of a circle is $176\text{ cm}$.
We have to find the radius of a circle.
Let us assume the radius of a circle is $r$ .

In the above diagram $AB=r$ is the radius of a circle.
Now, we know that circumference of a circle is equal to $2\pi r$.
Now as given in the question the circumference is $176\text{ cm}$.
So, equating the $2\pi r$to $176\text{ cm}$, we get
$2\pi r=176\text{ cm}$
Now, substitute the value $\pi ={\displaystyle \frac{22}{7}}$, we get
$2\times {\displaystyle \frac{22}{7}}\times r=176$
Now, solve further we get
$\Rightarrow {\displaystyle \frac{44}{7}}\times r=176$
Now, cross multiply to get the value of $r$
$\Rightarrow r=176\times {\displaystyle \frac{7}{44}}$
Now, we multiply $176$ with $7$ and divide the number obtained with $44$, we get
$\begin{array}{rl}& \Rightarrow r={\displaystyle \frac{1232}{44}}\\ & \Rightarrow r=28\text{ cm}\end{array}$
So, the radius of the circle is $28\text{ cm}$.

Note: The circumference of a circle is the arc length of the circle. In this question we use the value $\pi ={\displaystyle \frac{22}{7}}$ to solve the question. We know that the value of $\pi$ can be substituted either ${\displaystyle \frac{22}{7}}$ or $3.14$. But in this particular question we substitute $\pi ={\displaystyle \frac{22}{7}}$ because at the right hand side $176$ is easily divisible by $22$. If we put $\pi =3.14$ the calculation takes more time and it becomes lengthy.