Question

How do you find the circumference of a circle with a radius of 4 cm?

Answer 1

Hint: We must know the basic geometry of the circle to solve questions like this. Circumference of a circle is defined as the measure of the boundary of the circle, if we cut the boundary of the circle at one point and stretch it out as a straight line, then the length of that line will give us the circumference of the circle. It is usually measured in the standard units for measuring the length of an object, that is, cm, m, etc. Using this definition, we can find out the circumference of the circle.

Complete step-by-step answer:
A circle is a closed figure, as we go on increasing the number of sides of a closed polygon, we get nearer to a figure like a circle, and thus a circle has an infinite number of sides. The radius of a circle is the distance between the centre of the circle and any point lying on the circle.
We are given that the radius of the circle is 4 cm. We know that the circumference of the circle is given by the formula –
$circumference = 2\pi r$
On putting the value of r in the above formula, we get the circumference of the given circle as –
$
  circumference = 2 \times \pi \times 4 \\
   \Rightarrow circumference = 8\pi \,cm \;
 $
So, the correct answer is “$8\pi \,cm$”.

Note: Some of you might wonder how we got the formula for finding the circumference in terms of the pie. The formula for finding the circumference is derived by integration, at the end of the integration; the value comes in terms of the sine function, which gave us pie in the formula.