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GAOKAO · Solid Geometry · Advanced

Solid Geometry: Optimize cylinder in sphere math: max volume cylinder height? For math: height?

Sphere, cylinder, cone volume.

Try the problem

Optimize cylinder in sphere r=Rr=R: max volume cylinder height? For R=3R=\sqrt3: height?

Hint and answer

Concept to use

Composite solids.

Hint

Calc max; h=2R/3h=2R/\sqrt3 wait — classic h=2R/3h=2R/\sqrt3. For R=3R=\sqrt3, h=2h=2.

Answer

2

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