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Home > PC3 > Chapter 7 > Lesson 7.2.2 > Problem 7-90


Rectangle, with right side labeled, h, divided, with 3 dashed vertical lines, into 4 vertical rectangles, each bottom edge labeled, x, & 3 dimensional prism, front side, each edge labeled, x, right side, bottom edge labeled, h.A rectangular piece of cardboard has a perimeter of feet. The cardboard is creased in such a way that it can be folded to form a square tube with open ends as shown in the diagram.  

  1. Write an equation for the volume of the box in terms of and .

  2. Now, write the volume of the box using only .

  3. What is an appropriate domain for the function you wrote in part (b)?

    Of course . The 'largest' value of occurs when the height is approximately . Use your equation from part (a) to determine the largest possible value of .

  4. Graph the volume function and locate the point that represents the maximum volume.

    Use a graphing calculator to graph your equation from part (b).