Fixed Base

Fixed Base

The Volume of a rectangular prism with a square base is fixed at 120 cubic feet?

I need help figuring out this problem

Even though you know the volume, the formula is still useful.

V = x² h

where x is the side of the square base of the prism and h is the height of the prism. This gives you:

h = V/x²

The prism has 6 faces. The top and bottom are squares of side x, and the 4 sides are x-by-h rectangles, so:

A(x) = 2x² + 4xh = 2x² + 4x(V/x²)
A(x) = 2x² + 4V/x
A(x) = 2x² + (480 ft³)/x

That answers part A. Notice what happens to the second term when x goes to zero.

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