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K An open box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. Answers parts (a) through (e). (a) Express the volume V of the box as a function of the length x of the side of the square cut from each comer. V= (Simplify your answer.). (b) What is the volume if a 2-inch square is cut out? The volume is (Simplify your answer.) (c) What is the volume if a 6-inch square is cut out? The volume is (Simplify your answer.) (d) Graph V=V(x). For what value of x is V largest? Choose the correct graph below. O D. OA. B. n a a n 12 Xmin 0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl-25 Xmin=0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl=25 Xmin 0, Xmax 7.5, Xscl 0.5, Ymin 0, Ymax=275, Yscl=25 Xmin 0, Xmax=7.5, Xscl=0.5, Ymin=0, Ymax=130, Yscl For what value of x is V largest? (e) What is the largest volume? The largest volume is ☐

K An open box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. Answers parts (a) through (e). (a) Express the volume V of the box as a function of the length x of the side of the square cut from each comer. V= (Simplify your answer.). (b) What is the volume if a 2-inch square is cut out? The volume is (Simplify your answer.) (c) What is the volume if a 6-inch square is cut out? The volume is (Simplify your answer.) (d) Graph V=V(x). For what value of x is V largest? Choose the correct graph below. O D. OA. B. n a a n 12 Xmin 0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl-25 Xmin=0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl=25 Xmin 0, Xmax 7.5, Xscl 0.5, Ymin 0, Ymax=275, Yscl=25 Xmin 0, Xmax=7.5, Xscl=0.5, Ymin=0, Ymax=130, Yscl For what value of x is V largest? (e) What is the largest volume? The largest volume is ☐

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 92CR
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K An open box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. Answers parts (a) through (e). (a) Express the volume V of the box as a function of the length x of the side of the square cut from each comer. V= (Simplify your answer.). (b) What is the volume if a 2-inch square is cut out? The volume is (Simplify your answer.) (c) What is the volume if a 6-inch square is cut out? The volume is (Simplify your answer.) (d) Graph V=V(x). For what value of x is V largest? Choose the correct graph below. O D. OA. B. n a a n 12 Xmin 0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl-25 Xmin=0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl=25 Xmin 0, Xmax 7.5, Xscl 0.5, Ymin 0, Ymax=275, Yscl=25 Xmin 0, Xmax=7.5, Xscl=0.5, Ymin=0, Ymax=130, Yscl For what value of x is V largest? (e) What is the largest volume? The largest volume is ☐
Transcribed Image Text:K An open box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each corner and turning up the sides. See the figure. Answers parts (a) through (e). (a) Express the volume V of the box as a function of the length x of the side of the square cut from each comer. V= (Simplify your answer.). (b) What is the volume if a 2-inch square is cut out? The volume is (Simplify your answer.) (c) What is the volume if a 6-inch square is cut out? The volume is (Simplify your answer.) (d) Graph V=V(x). For what value of x is V largest? Choose the correct graph below. O D. OA. B. n a a n 12 Xmin 0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl-25 Xmin=0, Xmax 7.5, Xscl=0.5, Ymin=0, Ymax=275, Yscl=25 Xmin 0, Xmax 7.5, Xscl 0.5, Ymin 0, Ymax=275, Yscl=25 Xmin 0, Xmax=7.5, Xscl=0.5, Ymin=0, Ymax=130, Yscl For what value of x is V largest? (e) What is the largest volume? The largest volume is ☐
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