Back to Explain volume formulas — Problem 5 · Task Set 34

Exercises: Informal Arguments for Sphere Volume Using Cavalieri's Principle

Grade 10·22 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-gmd-a-2
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Fluency Practice

1.

For the cylinder-minus-cone comparison solid (cylinder radius rr, height rr; cone apex at base, base radius rr at top), at height hh the cone's inner radius equals   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . The annular cross-sectional area is Aannulus(h)=A_{\text{annulus}}(h) =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

cone's inner radius at height h:
annular area formula: