# Multivariable Calculus: Spheres and Cylindrical Surfaces Complete Lesson

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This lesson covers spheres and cylindrical surfaces for a Multivariable Calculus class. The equation of a circle is used to introduce the equation of a sphere. A review of "completing the square" is included to help students write the equation of a sphere in standard form. Students also get to practice drawing cylindrical surfaces in 3-space. Finally, inequalities help students develop additional intuition regarding spheres and cylindrical surfaces.

This lesson is meant for a Multivariable Calculus course, but it could be used in Geometry as part of a unit on three-dimensional geometry. No calculus is introduced in this lesson, although one of the homework problems is solved using calculus. Another option is to use it after AP Calculus exams have finished.

The topics covered include:
-The Equation of a Circle
-The Equation of a Sphere
-Writing the Standard Equation of a Sphere
-Practice with Finding the Equation of a Sphere
-Definition of a Cylindrical Surface
-Practice with Cylindrical Surfaces
-Inequalities in 3-Space
-Practice with Inequalities in 3-Space

In this product, you will find the following:
-Powerpoint Presentation (22 slides)
-Guided Notes (4 pages, a "filled in" copy is also included)
-Do Now Slips (4 slips on one page, answers included)
-Exit Ticket Slips (4 slips on one page, answers included)
-Homework Assignment (2 pages, a detailed answer key is included)

This lesson is part of a larger unit on The Geometry of Space. The complete unit includes the following:
-Working in Three Dimensions
-Spheres and Cylindrical Surfaces
-Lines and Planes
-Cylindrical Coordinates (coming soon!)
-Spherical Coordinates (coming soon!)
Total Pages
37 pages
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Teaching Duration
50 minutes
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\$6.50