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
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