A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides. a. Suppose the paper is 11"-wide by 15"-long. Let x 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 = (11-2x)*(15-2x)*x ii. If the cutout length increases from 0.7 to 2.1 inches, how much does the volume of the box change by? Preview cubic inches 62.832 iii. Estimate the maximum volume for this box? Tip: Use a graphing tool like www.Desmos.com cubic inches Preview 154.224 iv. What cutout length produces the maximum volume? | inches Preview b. Suppose we instead create the box from a 9"-wide by 12"-long sheet of paper. i. Estimate the maximum volume for this box? Tip: Use a graphing tool like www.Desmos.com cubic inches Preview Preview ii. What cutout length produces the maximum volume? Preview inches Preview

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