Question

How do you find the circumference of the circle with radius ${\text{3cm}}$?

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 solution:
Here we are given to find the circumference of the circle with radius${\text{3cm}}$ and for this, we must know what the meaning of the circumference of the circle is. So the 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 center and $d$ as its diameter and $R$ as its radius.

We know that diameter is the largest chord of the circle passing through centre and radius is half of the diameter. So we can say that:
${\text{Radius}} = \dfrac{{{\text{diameter}}}}{2}$$ = 3{\text{cm}}$$ - - - - (1)$
Now we are given that 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 $\pi d$ if he is given diameter in the question to get the length of the boundary as we know that $2R = d$
So as diameter$ = 6cm$
We get circumference as $6\pi {\text{ cm}}$.