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The rectangular iron sheet is 8 in length and 5 in width. Four identical cubes were cut off at four corners to make a small box without a lid. When the side is long, the volume of the box is the large
The rectangular iron sheet is 8 in length and 5 in width. Four identical cubes were cut off at four corners to make a small box without a lid. When the side is long, the volume of the box is the largest. solve

Let the side length of a square be x,

Volume: V=(8-2X)(5-2X)X

=40X-26X^2+4X^3

V'=40-52X+ 12X^2

Let V'=0,

40-52X+ 12X^2=0

(4X-4)(3X- 10)=0

4X-4=0, X 1= 1 (cm),

3X- 10=0, X2= 10/3 (cm), because the width direction is 5-2x = 15/3-20/3.

Therefore, when the side length of the small square is 1CM, the volume of the box is the largest.

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