Can you explain this formula in simple terms. I have the formula but I'm stuck. If you can't see the image, it's a circle that has a 10inch radius with arc BC 120°. I need to find the length of arc BDC. The answer should be 40/3π but I can't figure out how they got that.

Here's the formula:
L= m / 360° 2 π r
= 240° / 360° 2 π 10
= 40/3 π

Here's what i have so far:

360 - 120 = 240
240 / 360 = 0.666
The book says I then have to x by 2 then by 10 but my answer is 13.33. The correct answer should be 40/3π.

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Question

Can you explain this formula in simple terms.     I have the formula but I'm stuck.  If you can't see the image, it's a circle that has a 10inch radius with arc BC 120°.  I need to find the length of arc BDC.  The answer should be 40/3π but I can't figure out how they got that.

Here's the formula: 
L=  m / 360°  2 π  r  
= 240° / 360°   2 π 10
= 40/3 π

Here's what i have so far:

360 - 120  =   240
240 / 360  =   0.666
The book says I then have to x by 2 then by 10 but my answer is 13.33.  The correct answer should be 40/3π.

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anonymous · Answer

I think I figured it out.  
The answer is 40/3 =  13.33  
But if I wasn't given the answer, I'm still not sure how I would know that 13.33 is the quotient of 40/3.

directrix · Answer

@not_so_smart 

Here's the way I think about this type problem.

The degree measure of arc BDC is 240. That is 240/360 = 2/3 the perimeter of the circle.

The perimeter (circumference) of the circle is 2*pi*r.

 r = 10 in this problem so the perimeter of the circle is 20*pi.

Arc BDC is 2/3 of 20*pi = (40* pi)/3.