# The circumference of a circle is equal to 72 pi. Find the radius of this circle.

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Let the circumference of the circle be C = 72 pi

We know that the formula for the circumference is:

C = 2 * r * pi where r is the radius of the circle.

Then let us substitute with C to calculate the radius r:

==> 72 pi = 2* r * pi

Let us divide by pi both sides:

==> 72*pi / pi = 2*r * pi / pi

==> 72 = 2*r

Now divide by 2:

==> 72/2 = 2r/2

==> 36 = r

Then the radius of the circle is :

**r = 36 units**

We know that the ratio of the circumference and the diameter d is pi. The diameter d = two times radius. So d = 2r, where r is the radius.

Therefore circumference C = 2pi*r is the relation between the length of the circumference and the radius.

Given that circumference C = 72pi.

Therefore C = 2pi r = 72pi.

Therefore r = 72pi/2pi

r = 36.

Therefore the radius of the circle is 36.

GIVEN INFORMATION:

The circumference of the circle = 72* pi [pi = 3.14 or 22/7]

we know that C (circumference of the circle) = 2 * pi * r

where, r is the radius and pi is a Greek letter having a value of 22/7

or, 72 * pi = 2 * pi * r

or, r = 72 * pi / 2 *pi

**or, r = 36 units [Ans.]**