anonymous
  • anonymous
An open box is to be made from a square piece of cardboard of perimeter 20 cardboard by cutting four equal square pieces from each corner and turning up the sides. What is the ide length of the pieces that should be cut out so that the box will have maximum volume? A. 10" B. 10/3 " C. 3 " D. 5 "
Mathematics
chestercat
  • chestercat
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amistre64
  • amistre64
20/4 = 5 each side of your material is gonna be 5 wide; we need to remove an x by x piece from the sides so volume of the box is: Vb = x * (5-x-x) * (5-x-x) = x(5-2x)^2 = 4x^3 -20x^2 +25x To find the max volume we derive this to get: Vb' = 12x^2 -40x +25 Vb' = 0 = max
amistre64
  • amistre64
we can narrow the choice to B or C simply because they are improbable
amistre64
  • amistre64
plug in those values to Vb and see what you get :) 3(4(9) -20(3) + 25) 3(36 - 60 + 25) 3(1) = 3

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amistre64
  • amistre64
(10/3) (4(100/9) -20(10/3)+25) = 9.26 id go with b

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