Question #e5881

2 Answers
Jan 28, 2016

See explanation..

Explanation:

Remember that pi is the ratio between the diameter and the circumference of the circle.

If diameter is 1,circumference=pi
If 2,circumference=2pi

So,circumference of circle=pid,d=diameter

r=radius=d/2
So,d=2r

So,circumference of circle=2rpi,or,2pir

This is a simple poof that i think is the best

Jan 28, 2016

here is how you do it friend,

Explanation:

for this, we will need closed line integration.
suppose the radius of a circle is r
and after dt time it makes d theta angle in the center of the circle having the arc of dS
so,
dS=rd theta
now,
S=oint_0^(s)dS

=oint_0^(2pi)rd theta

=roint_0^(2pi)d theta

=r[theta]_0^(2pi)

=r[2pi-0]

=r2pi

=2pir