Question

The difference between circumference and diameter of a circle is $135cm$. Find the radius of the circle. Take $[\pi ={\displaystyle \frac{22}{7}}]$.

Answer 1

Hint: The diameter of a circle is double the radius of a circle. So, diameter can be written as $2r$. Similarly, we know that the perimeter of a circle is given as $2\pi r$. It is given that the difference between perimeter and diameter is $135cm$, we get $2\pi r-2r=135cm$. Solve the above equation to get the value of $r$.

Complete step-by-step answer:
It is given in the question that the difference between circumference and diameter of a circle is $135cm$ then, we have to find the radius of a circle. The value of $\pi$ is given as ${\displaystyle \frac{22}{7}}$. Let us assume that the radius of a circle is $r$. Then we know that the diameter of the circle is double the radius. So, the value diameter can be given as $2\times$radius.
We get the diameter of a circle $=2r$.
Now, we know that circumference of a circle is given by the formula $2\pi r$. Given the difference between circumference and diameter of a circle is $135cm$, which clearly means that the difference between $2\pi r$ and $2r$ is $135cm$. Then, we get
$2\pi r-2r=135cm$………………………………………….$(1)$
Taking $2r$ common in L.H.S, we get
$2r(\pi -1)=135$, substituting the value of $\pi$ as ${\displaystyle \frac{22}{7}}$, we get
$\Rightarrow 2r({\displaystyle \frac{22}{7}}-1)=135$
$\Rightarrow 2r\times \left({\displaystyle \frac{22-7}{7}}\right)=135$
$\Rightarrow 2r(15)=7\times 135$
$\Rightarrow 30r=945$
$\Rightarrow r={\displaystyle \frac{945}{30}}$
$\Rightarrow r=31.5cm$
Thus, the radius of a circle is of length $31.5cm$.

Note: If we know the circumference of a circle then we directly find the radius of a circle using formula, $r={\displaystyle \frac{circumference}{2\pi }}$. Where $\pi$ is the ratio of circumference and the diameter of a circle.