What you’ll learn
Identify 3D objects generated by rotations.
Key idea
A filled constant-width profile rotating a full turn gives constant circular cross-sections.
Axis length becomes height and perpendicular width becomes radius; changing axis interchanges roles.
Worked example
Classify examples and non-examples for the concept 'Identify 3D objects generated by rotations'.
A filled rectangle has horizontal width 3 and vertical height 4. It rotates one full turn about its horizontal side. Classify the solid and identify its radius and height.
- The named horizontal axis side has length 3, and perpendicular extent is 4.
- Each interior slice sweeps a filled disk of radius 4; constant radius gives a cylinder, not a tapering cone.
Answer: Cylinder, radius 4, height 3 — constant perpendicular width sweeps equal circular sections along the axis.
Quick Check
Classify examples and non-examples for the concept 'Identify 3D objects generated by rotations'.
A filled rectangle has horizontal width 5 and vertical height 4. It rotates one full turn about its vertical side. Classify the solid and identify its radius and height.