Question

A circle has a radius of \[6\,cm\]. What is its circumference?

Answer 1

Hint: We are given the radius of a circle and we need to find the circumference of the circle. Circumference of the circle is basically defined as the perimeter of the circle. To find the circumference of the circle, we use the formula \[2\pi r\], where \[r\] is the radius of the circle. Let us use this formula and find the circumference of the circle.

Complete step by step answer:
We are given the radius of the circle to be equal to \[6\,cm\]. We now draw this circle.

Here \[OA\] is the radius and hence, \[OA = 6cm\]. Now, we know,
Circumference of the circle \[ = 2\pi r\], where \[r\] is the radius of the circle.
Now, since radius is equal to \[6cm\], we get the value of \[r\] to be equal to \[6cm\] i.e. \[r = 6cm\]
Now, putting the value of \[r\] in the formula for the circumference, we get
\[ \Rightarrow \] Circumference of the circle \[ = 2\pi \left( {6cm} \right)\]
Opening the brackets, we get
\[ \Rightarrow \] Circumference of the circle \[ = 2\pi \times 6cm\]

As we know, Multiplication is associative, we can reshuffle the terms and get
\[ \Rightarrow \] Circumference of the circle \[ = 2 \times 6 \times \pi cm\]
Solving the above numeric value, we get
\[ \Rightarrow \] Circumference of the circle \[ = 12\pi cm\]
Now, putting the value of \[\pi \] equal to \[3.14\], we get
\[ \Rightarrow \] Circumference of the circle \[ = 12\left( {3.17} \right)cm\]
Multiplying the above number, we get
\[ \therefore \] Circumference of the circle \[ = 38.04\,cm\]

Hence, when the radius of the circle is \[6\,cm\], the circumference of the circle is equal to \[38.04\,cm\].

Note: First of all, we must be very clear with the terminology used for different shapes just like in this question, circumference of the circle is basically the perimeter of the circle. Note that, Area of the circle is given by the formula \[\pi {r^2}\] and circumference of the circle is given by \[2\pi r\], where \[r\] is the radius of the circle. If we were given the diameter instead of radius, we will first find the radius by using the formula \[r = \dfrac{d}{2}\], where \[r\] is the radius and \[d\] is the diameter, and then use radius in the formula.