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chris215
 one year ago
A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides.
What is the maximum volume this box could have? (Round your answer to two decimal places.)
chris215
 one year ago
A box is to be constructed from a sheet of cardboard that is 10 cm by 50 cm by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have? (Round your answer to two decimal places.)

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chris215
 one year ago
Best ResponseYou've already chosen the best response.1i got 2.36 is that right?

merchandize
 one year ago
Best ResponseYou've already chosen the best response.2So the box will have height x, length 10  2x, and width 50  2x, so we have: v = x(10  2x)(50  2x) v = x(500  20x  100x + 4x^2) v = 4x^3  120x^2 + 500x dv/dx = 12x^2  240x + 500 Set that to zero: 12x^2  240x + 500 = 0 x = ((240) +/ sqrt((240)^2  4*12*500)) / (2*12) x = (240 +/ sqrt(57600  24000)) / 24 x = (240 +/ sqrt(33600)) / 24 x = 10 +/ sqrt(175/3) But if x is greater than 5, the length of the box is negative, which doesn't make sense, so x can't be 10 + sqrt(175/3), which is approximately 17.6, so therefore x = 10  sqrt(175/3) =~ 2.36
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