(a)
To determine : Expressions for the length, width, and height of the open box.
The expressions for the length, width, and height of the open boxare
Given information :
A metal worker wants to make an open box from a sheet of metal, by cutting equal squares of side
Explanation :
The length of the box is given to be
Similarly, the width of the box is given to be
The height of the box will be
Therefore, the expressions for the length, width, and height of the open boxare
(b)
To determine : The function for the volume of the box.
The function for the volume of the box is
Given information :
A metal worker wants to make an open box from a sheet of metal, by cutting equal squares of side
Formula used:
Volume of cuboid = length
Explanation :
The expressions for the length, width, and height of the open boxare
Apply the formula for the volume of a cuboid.
Volume of cuboid = length
So, the volume of the box will be =
Therefore, the function for the volume of the box is
(c)
To calculate : The maximum volume of the box using graph and the side length of the cut-out squares that generates this volume.
The maximum volume of the box is
Given information :
A metal worker wants to make an open box from a sheet of metal, by cutting equal squares of side
Calculation :
The expressions for the length, width, and height of the open boxare
The function for the volume of the box is
So, the volume of the box is:
Draw the graph of the volume of the box.
So, the maximum volume of the box is
Therefore, the maximum volume of the box is
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education