A box with no top is to be built by taking a sheet of cardboard measuring 18-inches by 22-inches, cutting z-inch squares out ofeach corner, and folding up the sides.a) What are the length and width of the base of the box, after it is folded? It may help to draw a picture showing the cardboardbefore it is folded, and then draw another picture showing the resulting box.Length:b) What is the volume of the resulting box? Write your answer as a function of z.Volume:Width:c) What is the domain of this function? In other words, what values of a make sense? (Think about the original problem.)Domain:d) Find all of the critical points of this function (not just on the given domain).Critical points at: a =e) Find the absolute maximum of this function within its domain.Absolute maximum:cubic inchesf) What size squares should be cut out of the corners to maximize the volume of the resulting box?Size of squares: -inches wide squares

Answered: Image /qna-images/answer/2a9765d8-cd61-418d-b85b-3e9310c66308.jpg

A box with no top is to be built by taking a sheet of cardboard measuring 18-inches by 22-inches, cutting z-inch squares out of each corner, and folding up the sides. a) What are the length and width of the base of the box, after it is folded? It may help to draw a picture showing the cardboard before it is folded, and then draw another picture showing the resulting box. Length: b) What is the volume of the resulting box? Write your answer as a function of z. Volume: c) What is the domain of this function? In other words, what values of a make sense? (Think about the original problem.) Domain: Width: d) Find all of the critical points of this function (not just on the given domain). Critical points at: ==

A box with no top is to be built by taking a sheet of cardboard measuring 18-inches by 22-inches, cutting z-inch squares out of each corner, and folding up the sides. a) What are the length and width of the base of the box, after it is folded? It may help to draw a picture showing the cardboard before it is folded, and then draw another picture showing the resulting box. Length: b) What is the volume of the resulting box? Write your answer as a function of z. Volume: c) What is the domain of this function? In other words, what values of a make sense? (Think about the original problem.) Domain: Width: d) Find all of the critical points of this function (not just on the given domain). Critical points at: ==

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....

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