a.
To find: How long you should make the cuts?
The cuts should be
Given information:
You are making an open box to hold paper clips out of a piece of cardboard that is 5 inches by 8 inches. The box will be formed by making the cuts as shown in the diagram and folding up the sides. You want the box to have the greatest volume possible.
Formula used:
Volume of rectangular box is length times width times the height of the box.
Calculation:
The box will be formed by making the cuts of
The length of the box would be
To find the maximum volume, graph the volume function on a graphing calculator. Consider only the interval
It is visible that the maximum volume occurs when
b.
To find: What is the maximum volume of the box?
The maximum volume of the box would be
Given information:
You are making an open box to hold paper clips out of a piece of cardboard that is 5 inches by 8 inches. The box will be formed by making the cuts as shown in the diagram and folding up the sides. You want the box to have the greatest volume possible.
Formula used:
Volume of rectangular box is length times width times the height of the box.
Calculation:
From the graph in part (a), it is visible that the maximum volume is about
c.
To find: What will the dimensions of the finished box be?
The dimensions of the box will be
Given information:
You are making an open box to hold paper clips out of a piece of cardboard that is 5 inches by 8 inches. The box will be formed by making the cuts as shown in the diagram and folding up the sides. You want the box to have the greatest volume possible.
Formula used:
Volume of rectangular box is length times width times the height of the box.
Calculation:
To find the dimensions of box, use
Length of the box would be:
Width of the box would be:
Therefore, the dimensions of the box will be
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- 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