<PRE><B>Question 395600</B>
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(18)}}}; inches, side of the bar; this is also the diameter of the cylinder
Find the volume of the bar of iron
{{{sqrt(18)}}}*{{{sqrt(18)}}}*3 = 18*3 = 54 cu/inches, vol of the bar
:
Radius of the cylinder
r = {{{(sqrt(18))/2}}}
Volume of the cylinder
V = {{{pi*((sqrt(18))/2)^2*3}}}
V = {{{pi*(18/4)*3}}}
V = 42.41 cu/inches
:
Find the waste
54 - 42.41 = 11.6 cu/inches wasted</PRE>