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Find the exact length of the arc made by the central angle theta equals 22 degrees in a circle of radius r equals 18  μm.

 Aug 3, 2015

Best Answer 

 #1
avatar+118587 
+5

Arc length = (22/360) * 2pi*r

 

$${\frac{{\mathtt{22}}}{{\mathtt{230}}}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{18}} = {\mathtt{10.818\: \!006\: \!007\: \!143\: \!983\: \!7}}$$

 

Oh you wanted the exact length  :/

 

22 degrees = 22*pi/180 radians

 

    $$\\Arc\;\;length\\\\
=\frac{22\pi}{180}*2*\pi*18\\\\
=\left[\frac{22\pi}{180}\div (2\pi)\right]*2*\pi*18\\\\
=\left[\frac{22\pi}{180}\times \frac{1}{ (2\pi)}\right]*2*\pi*18\\\\
=\left[\frac{11}{180}\right]*2*\pi*18\\\\
=\frac{11\pi}{5}\;\micro \mu m\\$$

 Aug 3, 2015
 #1
avatar+118587 
+5
Best Answer

Arc length = (22/360) * 2pi*r

 

$${\frac{{\mathtt{22}}}{{\mathtt{230}}}}{\mathtt{\,\times\,}}{\mathtt{2}}{\mathtt{\,\times\,}}{\mathtt{\pi}}{\mathtt{\,\times\,}}{\mathtt{18}} = {\mathtt{10.818\: \!006\: \!007\: \!143\: \!983\: \!7}}$$

 

Oh you wanted the exact length  :/

 

22 degrees = 22*pi/180 radians

 

    $$\\Arc\;\;length\\\\
=\frac{22\pi}{180}*2*\pi*18\\\\
=\left[\frac{22\pi}{180}\div (2\pi)\right]*2*\pi*18\\\\
=\left[\frac{22\pi}{180}\times \frac{1}{ (2\pi)}\right]*2*\pi*18\\\\
=\left[\frac{11}{180}\right]*2*\pi*18\\\\
=\frac{11\pi}{5}\;\micro \mu m\\$$

Melody Aug 3, 2015

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