(a).
To write: The height
The height
Given information:
A right circular cylinder of radius
Calculation:
Use the Pythagorean Theorem in the right triangle and calculate the height below:
Therefore, the height
(b).
To write: The volume
The volume
Given information:
A right circular cylinder of radius
Calculation:
From the part (a),
Formula used:
The volume of the cylinder is given by
Substitute
Therefore, the volume
(c).
To find: The values of
The values of
Given information:
A right circular cylinder of radius
Calculation:
From the part (b),
For the domain of the volume, substitute the square root function is greater than or equal to zero and solve for
Therefore, the values of
(d).
To sketch: The graph
The graph of the volume
Given information:
A right circular cylinder of radius
Calculation:
From the part (b),
Now, draw the graph of the volume
below
(e).
To find: The maximum volume from the graph.
The maximum volume is equal to
Given information:
A right circular cylinder of radius
Calculation:
From the part (d),
The graph of the volume is below:
From the above graph, the maximum volume is
Therefore, the maximum volume is
Chapter 1 Solutions
Precalculus: Graphical, Numerical, Algebraic Common Core 10th Edition
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