Precalculus Module 3: Investigation 1 The Box Problem and Modeling Relationships *5. a. Using your graphing calculator, solve for the length of the side of the square cutout if the volume of the box is 62.5 cubic inches. b. Using your graphing calculator, solve for the length of the side of the square cutout if the volume of the box is 23 cubic inches. c. Using your graphing calculator, find an approximate maximum value for the box's volume. d. Using your graphing calculator, solve for the length of the side of the square cutout that produces the maximum volume you found in part (c). 6. An open box is constructed by cutting four equal-sized square corners from a 280 12-inch by 18-inch sheet of cardboard 260 and folding up the sides. The given graph 240 represents the volume of a box 220 (measured in cubic inches) in relation to 200 the length of the side of the square cutout e (in cubic inches) (measured in inches). 180 160 a. Determine the box's volume for each 140 given length of the side of the square box's volume ( 120 cutout. Use the graph to check that 100 your answer makes sense. i. 2 inches ii. 5 inches iii. 3.75 inches 0.5 b. Write a formula to represent the box's volume I (in cubic inches) in terms of x, the length of the side of the square cutout (in inches). c. Use the graph to estimate the length(s) of the side of the square cutout that produces each of the following volumes. i. 160 cubic inches ii. 190 cubic inches iii. 70 cubic inches d. Use the graph to determine the interval(s) for the length of the side of the square cutout over which the box's volume is decreasing as the cutout length increases. Then repeat for the interval(s) over which the box's volume is increasing as the cutout length increases. Pathways Precalculus 2018 Carlson, Oehriman, and Moore