An open box with a square base is to be made from a square

Chapter 2, Problem 25

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An open box with a square base is to be made from a square piece of cardboard 24 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. h 16 4 r 24 in. 24 in. x x x x x x x x (a) Express the volume V of the box as a function of the length x of the side of the square cut from each corner. (b) What is the volume if a 3-inch square is cut out? (c) What is the volume if a 10-inch square is cut out? (d) Graph V = V1x2. For what value of x is V largest?

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