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AP Calculus Lab
Maximum Volume of an Inscribed Shape
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Volume•Find the
volume of the largest right circular cone that can be inscribed in a sphere of radius “r”.
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Procedure
• Measure the sphere provided and develop a function for the inscribed cone’s volume.
• Determine the base and height dimensions that would yield the cone’s maximum volume.
• Construct a full scale model of your cone.• Fill your cone model with sand and record
the actual physical capacity of the cone.
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Review of the Basics
• You will need to develop the cone’s volume function in terms of the circle’s radius.
• The derivative of this function will yield the maximum volume desired.
v r h1
32
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Data Requirements
• Sketch of problem, with all pertinent components labeled.
• Explanation of your development of the volume function, and it’s components.
• Derivative operation. (Show your work)
• TI-83 graphs of the volume function and its derivative. (Use calculator’s maximum and zero menus to verify calculated results.)
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Shake it off and start the lab