Question

How do you find the circumference of the circle with a diameter of $6{\text{cm}}$?

Answer 1

Hint: Here we know that circumference is the boundary of the circle and it is given by the formula which is $2\pi R$ where $R$ is the radius of the circle. Hence we can simply apply this formula to get the value of the circumference of the circle.

Complete step-by-step answer:
Here we are given to find the circumference of the circle with a diameter of $6{\text{cm}}$ and for this we must know what the meaning of the circumference of the circle is. So circumference of the circle is actually the length of the boundary of the circle.
Similarly in rectangle and square we call the boundary length as the perimeter of the figure but only the terms are different for different shapes but the meaning is the same.
Let us consider the circle with $O$ as its centre and $d$ as its diameter and $R$ as its radius.

We know that diameter is the largest chord of the circle passing through the centre and radius is half of the diameter. So we can say that:
${\text{Radius}} = \dfrac{{{\text{diameter}}}}{2}$$ - - - - (1)$
As we have taken diameter as $d$ and the radius of the circle as $R$
We can write the above equation (1) as:
$R = \dfrac{d}{2}$$ - - - - (2)$
As we are given in problem that diameter of the circle is $6cm$ we can put this value in the equation (2) and get:
$R = \dfrac{6}{2} = 3cm$
Now we have got the radius of the circle as $3cm$
Now we know that circumference of the circle is given by the formula $2\pi R$
${\text{Circumference}} = 2\pi R$
Substituting the value of $R = 3cm$ in it we get:
${\text{Circumference}} = 2\pi (3) = 6\pi {\text{ cm}}$
We can further simplify this by putting the value of $\pi = 3.14$
So we get:
${\text{Circumference}} = 6\pi = 6(3.14) = 18.85{\text{ cm}}$

Note: Here a student can even apply directly the formula of circumference as $\pi d$ to get the length of the boundary as we know that $2R = d$
So as diameter$ = 6cm$
We get circumference as $6\pi {\text{ cm}}$