Question
An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminum and folding up the sides. Find the volume of the largest such box.
Solution
Let x metre be the length of a side of the removed squares. Then the height of the box is x, length is (8 – 2x) and breadth is (3 – 2 x).
Let V be the volume of the box.
For V to be maximum or minimum.
Rejecting x = 3 as breadth cannot be negative, we get,
Let V be the volume of the box.
For V to be maximum or minimum.
Rejecting x = 3 as breadth cannot be negative, we get,
