Explain volume formulas
Start lessonBegins with Cavalieris principle sphere volume · Slides
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
Teacher tools for this standard
Lesson Plan · Guided Notes · Exit Ticket · Re-teach · Homework
- Lesson Plan →Objectives, pacing and practice, built from this lesson's brief.
- Guided Notes →One page your students fill in and keep.
- Exit Ticket →Three items at the end of class. No student accounts.
- Re-teach →After an exit ticket: who missed what, and what to do tomorrow.
- Homework →Assign practice; it grades itself.
HSG.GMD.A.2
**HSG.GMD.A.2**: (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
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HSG.GMD.A.2: (+) Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.
What you'll learn
- State Cavalieri's principle and explain why solids with equal cross-sectional areas at every height have equal volumes
- Describe the classic comparison between a hemisphere and a cylinder-minus-cone composite solid
- Compute the cross-sectional area of a hemisphere at an arbitrary height h and show it equals the annular cross-section of the cylinder-minus-cone
- Derive the volume formula V = (4/3)pi r^3 for a sphere using the hemisphere argument and Cavalieri's principle
- Apply Cavalieri's principle informally to compare volumes of other solid figures such as prisms and oblique cylinders
Review first:
Slides
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1
Cavalieris principle sphere volume
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