You are planning to make an open rectangular box from a 12 by 14 cm piece of cardboard by cutting congruent squares from the corners and folding up the sides.
A) what are the dimensions of the box of largest volume you can make this way?
B) what is the volume?
1
Expert's answer
2011-02-09T10:14:07-0500
Denote the side of the square as x. The volume of the box would be V = x*(12-2x)*(14-2x) = 4x3 - 52x2 + 168x Let's find the roots of first derivation dV/dx: V' = 12x2 - 104x + 168 = 0: x1 = 2 (13-2√37)=1.67 and x2 = 2(13 + 2√37)= 50.33 > 14 Thus the dimentions of the box would be: {8.66, 10.66, 1.67}.
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