SOLUTION: find the waste in making the largest possible cylindrical rod from a bar of iron 3 feet long which has a square cross section whose diagonal is 6 inches

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Question 395600: find the waste in making the largest possible cylindrical rod from a bar of iron 3 feet long which has a square cross section whose diagonal is 6 inches
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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find the waste in making the largest possible cylindrical rod from a bar of iron
3 feet long which has a square cross section whose diagonal is 6 inches
:
Find the length of the sides (x) of the square cross section
x^2 + x^2 = 6^2
2x^2 = 36
x^2 = 18
x = sqrt%2818%29; inches, side of the bar; this is also the diameter of the cylinder
Find the volume of the bar of iron
sqrt%2818%29*sqrt%2818%29*3 = 18*3 = 54 cu/inches, vol of the bar
:
Radius of the cylinder
r = %28sqrt%2818%29%29%2F2
Volume of the cylinder
V = pi%2A%28%28sqrt%2818%29%29%2F2%29%5E2%2A3
V = pi%2A%2818%2F4%29%2A3
V = 42.41 cu/inches
:
Find the waste
54 - 42.41 = 11.6 cu/inches wasted