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An open box with a square base is to be made out of a given cardboard of area c2(square) units. Show that the maximum volume of the box is c3/6√3 (cubic) units.

1 Answer

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Best answer

Consider each side of base a and h as the height

So we get c2 = (a2 + 4ah)

It can be written as

h = (c2 – a2)/4a

Here volume can be written as

V = a2 × h

By substituting the value of h

V = (c2a – a3)/ 4

By differentiating w.r.t a

Which is lesser than 0

Hence, V is maximum when a2 = c2/3 and h = c/23

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