(8,7,11) Figure 1 Figure 2 A(n) 3 in x 12 in piece of cardboard has squares cut out of each corner in order to make a box (see Figure 1). Let z represent the length of a cut-out square (the height of the box). (a) Find a function V(z) for the volume of the box in terms of z. V(z) (b) Find the domain of the function. Write your answer as a compound inequality involving z. Domain of V(z): (c) Using the graph of V(z) shown in Figure 2, determine the dimensions that yield the maximum volume. Round your answers to the nearest tenth. Height: in Width: in Length: in

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