Mathematics: Arectangular box has a square base. if the sum of the height and the perimeter of the square base is 12 in, what is the maximum possible volume?

Arectangular box has a square base. if the sum of

jessicagustama

13.03.2022

Let the square base has length and the height of the box be . It is given that $4b+h=12\\ h=4(3-b)$

The volume of the box is V=b^2h=4b^2(3-b) .

For maximum volume $\frac{dV}{db} =0\\ \frac{d(4b^2(3-b))}{db} =0\\ 6b-3b^2=0\\ b=2$

The maximum possible volume occurs when b=3 in .

$V_{max} =4(2)^2(3-2) =16 in^3$

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