To identify the pattern in which the dimensions of the box changes and to find the volume of the extra-large box which is one size larger than the third box.
From the given pattern of boxes, it is observed that the width of the boxes remains the same:
Since the extra-large box is formed out of the third box by expanding it by
Then, the volume
Given:
Given the boxes:
Also, it is given that the extra-large box is one size greater than the third one.
Concept Used:
Volume of a rectangular prism:
Suppose that
Calculation:
Determine the pattern of change in the dimension of boxes:
From the given pattern of boxes, observe that the width of the boxes remains the same:
Now, both the height and the length of the boxes increase by
Thus, the width
Also, the length
Thus, the length
That is, the length
Find the volume of the extra-large box:
The dimensions of the extra-large box is found:
Then, the volume
Thus, the volume of the extra-large box is
Conclusion:
From the given pattern of boxes, it is observed that the width of the boxes remains the same:
Since the extra-large box is formed out of the third box by expanding it by
Then, the volume
Chapter 1 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