SOLUTION: A box is to be constructed from a sheet of cardboard that is 20 cm by 60 cm, by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum

Question 987179: A box is to be constructed from a sheet of cardboard that is 20 cm by 60 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?
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The 20cm side would become long.
The 60cm side would become long.
The total volume of the box would be

To find the maximum volume, take the derivative and set it equal to zero.

Of the two values, only is in the range of x which can only have values between and since must remain positive.
So then the maximum volume that the box can have is,

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