Question #e5881

2 Answers
Jan 28, 2016

Answer:

See explanation..

Explanation:

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

If diameter is #1,ci##rcumference=pi#
If #2,ci##rcumference=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

Answer:

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#