Lesson Plan

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

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.