Question

If the difference between the circumference and the radius of the circle is 37 cm, then find the circumference of the circle. $\left( {\pi = \dfrac{{22}}{7}} \right)$
A) 154
B) 44
C) 14
D) 7

Answer 1

Hint: First of all make the equation in r using the data: the difference between the circumference and the radius of the circle is 37 cm and find r using this. Then put it in the formula of circumference and thus, we have got the required answer.

Complete step-by-step answer:
We will need to use the formula for the circumference of the circle.
We know that $Circumference = 2\pi r$, where r is the radius of the circle.
We are given in the question that: the difference between the circumference and the radius of the circle is 37 cm.
Writing the same mathematically, we will have:-
$2\pi r - r = 37$
Taking r common on the LHS, we have:-
$r(2\pi - 1) = 37$
Now putting the value of $\pi $ as given in the question, we will get:-
$r\left( {2 \times \dfrac{{22}}{7} - 1} \right) = 37$
Simplifying the same further:-
$r\left( {\dfrac{{44}}{7} - 1} \right) = 37$
Taking LCM on LHS, we will get:-
$r\left( {\dfrac{{44 - 7}}{7}} \right) = 37$
Simplifying it further:-
$r\left( {\dfrac{{37}}{7}} \right) = 37$
$ \Rightarrow r = 37 \times \dfrac{7}{{37}} = 7cm$
Hence, we have the radius as 7 cm.
Now, we need to find the circumference of the circle.
So, putting the value of r = 7cm in the formula:-
$Circumference = 2\pi r$, where r is the radius of the circle.
So, we have:- $Circumference = 2 \times \dfrac{{22}}{7} \times 7 = 44cm$.

Hence, the correct option is (B).

Note: The students must make sure that they use the value of $\pi $ as mentioned in the question. Sometimes, they might tend to use 3.14 to simplify it more but take care and do as given in the question.
We can avoid using the formula again for the circumference and just put in the value of r in the given equation:- Circumference - r = 37 and by putting in r = 7, we will have:- Circumference = 37 + 7 = 44.
We must know that Circumference is a kind of perimeter only which means the boundary of the circle.
Fun Fact:- A circle has the shortest perimeter of all shapes with the same area.