Concept explainers
a.
To write: An expression for l in terms of r .
Given information:
You have 600 square feet to material for building a greenhouse that is shaped like half a cylinder. The surface area S of the greenhouse 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 greenhouse is given by
Calculation:
To obtain the required equation use
Therefore, the required equation would be
c.
To graph: The volume function from part (b). What are the dimensions of r and l that maximize the volume of the greenhouse? What is the maximum volume?
The maximum volume of the greenhouse would be approximately 1596 cubic feet.
Given information:
The volume V of the greenhouse 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 l would be 15.87 feet.
Chapter 2 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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