SOLUTION: Please solve:
In an Equilateral triangle with each side 8cm. Overlapping the triangle there are circular arcs, each of radius 2cm are drawn as shown below. Calculate the total arc
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Question 975726: Please solve:
In an Equilateral triangle with each side 8cm. Overlapping the triangle there are circular arcs, each of radius 2cm are drawn as shown below. Calculate the total arc lengths of the curved shape.
This is the diagram, you just need to put the numbers in: https://fbcdn-sphotos-f-a.akamaihd.net/hphotos-ak-xat1/t31.0-8/11536418_580827295391051_3659053882599517983_o.jpg
Found 2 solutions by Alan3354, Fombitz:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
There are 3 1/2 circles r = 2 cm
The 3 internals arcs are 60 degs each.
3*60 = a 4th 1/2 circle.
Sum of 2 circles r = 2 cm
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2*2pi*2 = 8pi cms
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
I'm assuming that the 2 cm radii are centered at the vertices.
So then as you go across any leg you have 2 cm radius, diameter of larger circle, and then another 2 cm radius.
The are length of the semicircles outside of the triangle would be three times half the circumference of the entire circle,
.
.
The arc lengths of the internal circles are obtained using the arc length formula since each vertex is 60 degrees or radians.
So the total length is,
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