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

32

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