Question #e5881

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Question #e5881

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Answer 1 · 2016-01-28T13:40:03

See explanation..

Explanation:

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

If diameter is $1, c i$ $1,ci$ $r c u m f e r e n c e = π$ $rcumference=pi$
If $2, c i$ $2,ci$ $r c u m f e r e n c e = 2 π$ $rcumference=2pi$

So,circumference of circle= $π d$ $pid$ $, d = d i a m e t e r$ $,d=diameter$

$r = r a d i u s = \frac{d}{2}$ $r=radius=d/2$
So, $d = 2 r$ $d=2r$

So,circumference of circle= $2 r π, or, 2 π r$ $2rpi,or,2pir$

This is a simple poof that i think is the best

Answer 2 · 2016-01-28T13:44:52

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 $d t$ $dt$ time it makes $d θ$ $d theta$ angle in the center of the circle having the arc of $d S$ $dS$
so,
$d S = r d θ$ $dS=rd theta$
now,
$S = \oint_{0}^{s} d S$ $S=oint_0^(s)dS$

$= \oint_{0}^{2 π} r d θ$ $=oint_0^(2pi)rd theta$

$= r \oint_{0}^{2 π} d θ$ $=roint_0^(2pi)d theta$

$= r {[θ]}_{0}^{2 π}$ $=r[theta]_0^(2pi)$

$= r [2 π - 0]$ $=r[2pi-0]$

$= r 2 π$ $=r2pi$

$= 2 π r$ $=2pir$

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Question #e5881

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