What is the relationship between a hemisphere, a cone, and a cylinder? Using Cavalieri's Principle, the class determines that the sum of the volume of a hemisphere and a cone with the same radius and height equals the volume of a cylinder with equal radius and height. The lesson continues to incorporate the volume formula to derive the formula for the surface area of a sphere. 

Concepts

spheres, volume of spheres, surface area

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Additional Tags

math

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Instructional Ideas

• Research and find visuals of Cavalieri's Principle proof of the volume of a sphere that can be projected to show the class during the discussion
• It may be beneficial to split the lesson into two days, one day for the volume and one day for the surface area

Classroom Considerations

• The concept may be difficult to grasp without being able to see it; add visuals to make the lesson more understandable
• The twelfth lesson in a 14-part series

Pros

• Includes a graphic organizer that is commonly used with vocabulary
• Provides some images that will be helpful to those struggling to envision what is being discussed

Cons

• None

Common Core

HSG-GMD.A.1 HSG-GMD.A.2 HSG-GMD.A.3 HSG-GMD.B.4 HSG-MG.A.1 HSG-MG.A.3 MP1 MP7