Max/Min Example 2
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Max/Min Example 2
A container in the shape of a right circular cylinder with no top has a surface area of 3pi sq ft. Express the volume as a function of r.
Reread the Problem
A container in the shape of a right circular cylinder with no top has a surface area of 3pi sq. ft.Express the volume as a function of r.
Visualize the Situation
It should be evident that a right cylinder (a can) has the following geometric shapes: 2 circles - the top and bottom. (In this problem, there is only 1 circle - the bottom.) 1 rectangle - if you cut the can along its seam, and flatten it out, its shape would be a rectangle.
Visualize the Situation Con't
· The opened-top cylinder, as noted, consists of two geometric shapes
· Rectangular Frame Its perimeter formula Its area formula
· Circular Bases Its circumference formula Its area formula
Identify What Is Given
The problem states that this is a right circular cylinder that has a surface area of 3pi sq. ft. So, what is given?
What Do You Already Know?
We know we can build the surface area formula with what we already know: The area of a circle and the area of a rectangle.
The Secondary Equation is...
What Are You Looking For?
The Problem: A container in the shape of a right circular cylinder with no top has a surface area of 3pi sq ft. Express the volume as a function of r.
Looking for: Volume in terms of r
The Volume Formula is thePrimary Equation
Write the Secondary Equation in Terms of r
Secondary Equation
Rewrite in terms of r
What will you do next?
Plug the Secondary Expression into the Primary Equation
Find the Solution to the Problem. Ask Yourself...
Click on the correct question.
· Are you finding the max/min?
· Are you finding the values of the variables? (i.e. length/width)
· Are you asked to find the max/min and where the max/min occurs?
· Are you asked to find an expression in terms of one variable?
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Max/Min Example 2
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Created on March 13, 2021
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Transcript
Max/Min Example 2
Return to NazPrecSum
Max/Min Example 2
A container in the shape of a right circular cylinder with no top has a surface area of 3pi sq ft. Express the volume as a function of r.
Reread the Problem
A container in the shape of a right circular cylinder with no top has a surface area of 3pi sq. ft.Express the volume as a function of r.
Visualize the Situation
It should be evident that a right cylinder (a can) has the following geometric shapes: 2 circles - the top and bottom. (In this problem, there is only 1 circle - the bottom.) 1 rectangle - if you cut the can along its seam, and flatten it out, its shape would be a rectangle.
Visualize the Situation Con't
· The opened-top cylinder, as noted, consists of two geometric shapes
· Rectangular Frame Its perimeter formula Its area formula
· Circular Bases Its circumference formula Its area formula
Identify What Is Given
The problem states that this is a right circular cylinder that has a surface area of 3pi sq. ft. So, what is given?
What Do You Already Know?
We know we can build the surface area formula with what we already know: The area of a circle and the area of a rectangle.
The Secondary Equation is...
What Are You Looking For?
The Problem: A container in the shape of a right circular cylinder with no top has a surface area of 3pi sq ft. Express the volume as a function of r.
Looking for: Volume in terms of r
The Volume Formula is thePrimary Equation
Write the Secondary Equation in Terms of r
Secondary Equation
Rewrite in terms of r
What will you do next?
Plug the Secondary Expression into the Primary Equation
Find the Solution to the Problem. Ask Yourself...
Click on the correct question.
· Are you finding the max/min?
· Are you finding the values of the variables? (i.e. length/width)
· Are you asked to find the max/min and where the max/min occurs?
· Are you asked to find an expression in terms of one variable?
Return To NazPrecSum