a.
To write: An expression for h in terms of r .
Given information:
A zookeeper is building a cylindrical habitat for alligators. He has 4000 square feet of waterproof material use. The habitat will not need a roof. The surface area (in square feet) of the habitat is given by
Calculation:
Substitute
Therefore, the required expression would be
b.
To write: An equation that given V as a polynomial function of r alone.
Given information:
The volume V of the habitat is given by
Calculation:
To obtain the required equation use
Therefore, the required function would be
c.
To graph: The volume function from part (b). What are the dimensions of r and h that maximize the volume of the habitat? What is the maximum volume?
The maximum occurs, when
The maximum volume of the habitat would be approximately
Given information:
The volume V of the habitat is given by
Calculation:
Upon graphing the volume function, the required graph would look like as shown below:
Upon looking at the graph, it is visible that the maximum volume is approximately
Therefore, the value of h would be
d.
To find: Which value of r did you have to reject when finding the maximum volume? Why?
Any value less than 0 will be rejected while finding the maximum volume.
Given information:
A zookeeper is building a cylindrical habitat for alligators. He has 4000 square feet of waterproof material use. The habitat will not need a roof. The surface area (in square feet) of the habitat is given by
Calculation:
The negative values or values less than 0 will be rejected while finding the maximum value. It is because radius cannot be negative.
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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