1. 4.5 Spheres a la Archimedes

2.  Objectives ◦ Derive the formula for the volume of a sphere

3. Problem 1 Starting with Circles … and Cones

4.  Sphere: Set of all points in three dimensions that are equidistant from a center point  Radius of a Sphere: Segment drawn from the center of a sphere to any point on the sphere  Diameter of a Sphere: Segment drawn connecting any two points on the circle passing through the center

5.  Cross Section: The 2-D “Slice” when a plane passes through the object  The cross section of a sphere is a circle  Great Circle of a Sphere: A cross section when a plane passes through the center ◦ Longitude lines are great circles  Hemisphere: Half of a sphere

6.  Collaborate 1-2 (3 Minutes)  Together #3  Annulus: The area between two concentric circles

8.  Hemisphere: Half of a sphere  Together: Volume of a Hemisphere

9. Remember The radius of the base is equal to the height h = r