the box
Algebra
Level
2
From a square piece of cardboard measuring 2a on each side a box with no top is to be formed by cutting out from each corner a square with sides b and bending up the flaps, For what value of b will the box contain the greatest volume?
2a
2a/3
a/3
a/76
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1 solution
Volume of the box is 4 b ( a − b ) 2 , which is maximum when a − b = 2 b or b = 3 a