Solid Geometry (Advanced)

Solid Geometry: core idea

• 1. Skew lines in cube opposite edges: distance if edge $2$?

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• 2. Sphere ∩ plane through center: circle radius if sphere $r=5$?

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

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• 4. Truncated cone volumes — $r=2,R=4,h=6$: volume $/\pi$?

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• 5. Rotate $y=\sqrt{x}$ $0..1$ about $y$-axis: volume $/\pi$ (shells)?

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• 6. Dihedral of cube adjacent faces degrees?

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• 7. Vector: volume parallelepiped edges $\langle1,0,0\rangle,\langle0,1,0\rangle,\langle0,0,2\rangle$?

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• 8. Prove right angle: vectors $\langle1,0\rangle,\langle0,1\rangle$ dot?

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• 9. Cross section triangle prism: equilateral side $2$ area?

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