A box is formed by cutting squares from the four corners of a sheet of paper and földing up the sides. a. Suppose the paper is 11"-wide by 13"-long. Let a represent the length of the side of the square cutout (in inches), and let V represent the volume of the box (in cubic inches). i. Write a formula that expresses V in terms of x. V = x(11-2x)(13-2x) ii. If the cutout length increases from 0.5 to 2.6 inches, how much does the volume of the box change by? * cubic inches Preview iii. Estimate the maximum volume for this box? Tip: Use a graphing tool like www.Desmos.com. * cubic inches Preview iv. What cutout length produces the maximum volume? * inches Preview b. Suppose we instead create the fox from a 5"-wide by 7"-long sheet of paper. i. Estimate the maximum volume for this box? Tip: Use a graphing tool like www.Desmos.com. Preview cubic inches Preview ii. What cutout length produces the maximum volume? Preview inches Preview

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