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
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter39: Symbolism And Algebraic Expressions
Section: Chapter Questions
Problem 5A
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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
Transcribed Image Text:X
X
X
Figure 1
Value of x that maximizes volume:
Maximum volume:
---
9
X
X
in
0 in
3
Figure 2
X S
?
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