ap calculus lab maximum volume of an inscribed shape

AP Calculus Lab

Maximum Volume of an Inscribed Shape

Volume•Find the

volume of the largest right circular cone that can be inscribed in a sphere of radius “r”.

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.

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

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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.)

Shake it off and start the lab