
Concept explainers
(a.)
A labelled diagram of the sculpture in terms of
A labelled diagram of the sculpture in terms of
Given:
A sculpture is shaped as a pyramid with a square base.
The height of the pyramid is
The volume of the sculpture is
Concept used:
Assuming an unknown dimension as
Calculation:
Let
It is given that the height of the pyramid is
Then, the height of the pyramid shaped sculpture is
Now, a labelled diagram of the sculpture is given as follows,
Conclusion:
A labelled diagram of the sculpture in terms of
(b.)
A function that gives the volume
It has been determined that the function that gives the volume
Given:
A sculpture is shaped as a pyramid with a square base.
The height of the pyramid is
The volume of the sculpture is
Concept used:
The volume
Calculation:
As assumed previously,
Then, the area of the square base (in square inches) is given as
Now, according to the discussed formula, the volume
Rewriting,
This is the required function that gives the volume
Conclusion:
It has been determined that the function that gives the volume
(c.)
The graph of the function obtained in part (b) and the estimate of the value of
The graph of the function obtained in part (b) is given as:
It has been determined that the estimate of the value of
Given:
A sculpture is shaped as a pyramid with a square base.
The height of the pyramid is
The volume of the sculpture is
Concept used:
If either the abscissa or the ordinate is known, the corresponding ordinate or the abscissa can be obtained from the graph of the function.
Calculation:
The function obtained in part (b) is,
The graph of this function is given as,
It is given that the volume of the sculpture is
So,
It can be seen from the graph that
This is the required estimate.
Conclusion:
The graph of the function obtained in part (b) is given as:
It has been determined that the estimate of the value of
(d.)
The value of
The value of
It has been determined that the base of the sculpture is
Given:
A sculpture is shaped as a pyramid with a square base.
The height of the pyramid is
The volume of the sculpture is
Concept used:
An equation can be solved by factorizing.
Calculation:
The function obtained in part (b) is,
It is given that the volume of the sculpture is
So,
Put
Simplifying,
On further simplification,
Finally,
Factorizing,
Note that the discriminant of
This implies that the roots of
So, the only real root of the obtained equation is
Now, the estimated value from part (c.) was also
As assumed in part (a), the length of a side of the square base is
So, the base of the sculpture is
Conclusion:
The value of
It has been determined that the base of the sculpture is
Chapter 2 Solutions
Mcdougal Littell Algebra 2: Student Edition (c) 2004 2004
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