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Sagot :
Answer:
L = 6 * ( π + 1 )
Explanation:
The side of the equilateral triangle is 4, and each one of the circles is of radius 1. Then
Triangle vertex A B and C
Trajectory of the belt, beginning in vertex A
1.-First circle A one turn
L₁ = 2*π*1 = 2*π
2.-Length between the circle A and B
L₂ = 2
3.- To wrap this circle we need to wrap the circle and to run the belt through the radius twice. The firs over the side AB and the second over the side BC, therefore
L₃ = 2*π*1 + 2*(1)
L₃ = 2*π + 2
4.-Length between two nearest points of circles B and C is 2 and length of the circle in C is 2*π*1. Then
L₄ = 2 + 2*π
Total length of the belt is:
L = L₁ + L₂ + L₃ + L₄
L = 2*π + 2 + (2*π + 2 ) + ( 2 + 2*π )
L = 6*π + 6
L = 6 * ( π + 1 )
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