Answer:
Temperature T = 394.38 K
Explanation:
The full solution and detailed explanation regarding the above question and its specified conditions can be found below in the accompanying document. I trust my explanation will assist you in grasping this particular topic.
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Response:
The cutting speed is calculated at 365.71 m/min
Clarification:
Given parameters include
diameter D = 250 mm
length L = 625 mm
Feed f = 0.30 mm/rev
cut depth = 2.5 mm
n = 0.25
C = 700
To find
the cutting speed that ensures the tool life coincides with the cutting time for the three parts
The formula for cutting time is given as
Tc =
....................1
where D refers to diameter, L refers to length and f refers to feed while V represents speed 
Thus, we derive
Tc = 
Tc = 
Given the tool life is expressed as
T = 3 × Tc............................2
where T denotes tool life and Tc is the cutting duration
Calculating tool life by substituting values into equation 2 yields
T = 3 × 
According to the Taylor tool formula, cutting speed is expressed as

× V × 8.37 = 700
This yields V = 365.71
Thus, the cutting speed calculates to 365.71 m/min
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