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Learning Goal
Part of: Explain volume formulas and use them to solve problems — 2 of 3 cluster items
Explain volume formulas
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
Prerequisites
Slides
Interactive presentations perfect for visual learners • Interactive presentation
Slide Video
Watch narrated slides play like a video lesson • Narrated slide playback
Exercises
Practice problems to build fluency and understanding • 1 exercises