A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 4 in. by 9 in. Six squares will be cut from the cardboard: one square will be cut from each of the corners, and one square will be cut from the middle of each of the 9 in. sides. (Fig. 1) The remaining cardboard will be folded to form the box and its lid. (Fig. 2) Letting x represent the side lengths in inches of the squares, find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round responses to two decimal places. Value of x that maximizes volume: ____in. Maximum volume: _____in^3

A box with a hinged lid is to be made out of a rectangular piece of cardboard that measures 4 in. by 9 in. Six squares will be cut from the cardboard: one square will be cut from each of the corners, and one square will be cut from the middle of each of the 9 in. sides. (Fig. 1) The remaining cardboard will be folded to form the box and its lid. (Fig. 2) Letting x represent the side lengths in inches of the squares, find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round responses to two decimal places. Value of x that maximizes volume: in. Maximum volume: _in^3

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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