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[tex]\\ \text{Given a box with fixed volume V.}\\ \text{and the base of the box is a square of side length b.}\\ \\ \text{we need to find the formula for the height, h, of the box as a function of b.}\\ \\ \text{We know that the volume of the box is given by}\\ \\ V=\text{Length }\times \text{ Width}\times \text{ Height}\\ \\ \text{Here since the base is square, so Length = Width = b}\\ \\ \text{so we have}\\ \\ V=b\times b\times h\\ \\ \Rightarrow V=b^2h\\ \\ \Rightarrow h=\frac{V}{b^2}[/tex]
Hence the formula for the height, h is : h=[tex]\frac{V}{b^{2} }[/tex]
Formula for height of the given box as a function of b is;
h = V/b²
We are dealing with a box here and so it will have length, width and height.
Length = l
breadth = b
Height = h
Since the base of the box is a square, it means that the length is equal to the width.
Now, formula for volume of a cube is;
V = lbh
Since l = b and we want to express h in terms of V and b, then we have;
V = b × b × h
V = b²h
h = V/b²
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