(13 Suppose you want to make a rectangular cardboard box with no top by cutting out squares in the corners of a flat piece of cardboard, bending it up to make the sides, and taping them. (a) If your flat piece of cardboard is 8 feet by 6 feet, give the dimensions of two different size boxes you could make. (b) Could you make a box with a surface area of 48 square feet? If so, what are the dimensions? If not, why not? (c) Could you make a box with a surface area of 32 square feet? If so, what are the dimensions? If not, why not? (d) If you cut a length of 2 feet out of the flat piece, what will the volume of the box be? (e) If you cut a length of x feet out of the flat piece, give an expression for the volume of the box. (f) Use a graphing device of some sort and sketch the graph of your volume equation found above. Use the graph to answer the following question: Is it possible to make a box whose volume is 25 cubic feet?

(13 Suppose you want to make a rectangular cardboard box with no top by cutting out squares in the corners of a flat piece of cardboard, bending it up to make the sides, and taping them. (a) If your flat piece of cardboard is 8 feet by 6 feet, give the dimensions of two different size boxes you could make. (b) Could you make a box with a surface area of 48 square feet? If so, what are the dimensions? If not, why not? (c) Could you make a box with a surface area of 32 square feet? If so, what are the dimensions? If not, why not? (d) If you cut a length of 2 feet out of the flat piece, what will the volume of the box be? (e) If you cut a length of x feet out of the flat piece, give an expression for the volume of the box. (f) Use a graphing device of some sort and sketch the graph of your volume equation found above. Use the graph to answer the following question: Is it possible to make a box whose volume is 25 cubic feet?

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

(13) Suppose you want to make a rectangular cardboard box with no top by cutting out squares
in the corners of a flat piece of cardboard, bending it up to make the sides, and taping them.
(a) If your flat piece of cardboard is 8 feet by 6 feet, give the dimensions of two different
size boxes you could make.
(b) Could you make a box with a surface area of 48 square feet? If so, what are the
dimensions? If not, why not?
(c) Could you make a box with a surface area of 32 square feet? If so, what are the
dimensions? If not, why not?
(d) If you cut a length of 2 feet out of the flat piece, what will the volume of the box be?
(e) If
you cut a length of x feet out of the flat piece, give an expression for the volume of
the box.
(f) Use a graphing device of some sort and sketch the graph of your volume equation found
above. Use the graph to answer the following question: Is it possible to make a box
whose volume is 25 cubic feet?

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