# Maximizing the Volume and Surface Area of Geometric Solids Inscribed in a Sphere

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This Demonstration illustrates two common types of max-min problem from a Calculus I course—those of finding the maximum volume and finding the maximum surface area of a geometric figure inscribed in a sphere. The figures available are a cylinder, a cone, and a cuboid with a square base. The sphere has radius 1. For the cylinder and the cone, *r* is the radius of the base. For the cuboid, *r *is one-half the length of a side of the base. An option to show the projection of the sphere and the inscribed solid onto the - plane is included (see snapshot 5).

Contributed by: Marc Brodie (Wheeling Jesuit University) (March 2011)

Open content licensed under CC BY-NC-SA

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