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From a square piece of card-board measuring $2a$ on each side of 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. The value of $b$ for which the box has the greatest volume is

  1. $b= \frac{a}{5}$
  2. $b= \frac{a}{4}$
  3. $b= \frac{2a}{3}$
  4. $b= \frac{a}{2}$
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