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