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Cylinders: The Curvilinear Solid

Exploring the shape that powers engines and stores fluids.

A Cylinder is a three-dimensional solid that holds two parallel circular bases at a fixed distance. It is one of the most common curvilinear geometric shapes.

Archimedes and the Cylinder

The great mathematician Archimedes (287–212 BC) considered his work on the cylinder to be his greatest achievement. He proved that the volume of a sphere is exactly two-thirds the volume of a cylinder that encloses it. He was so proud of this discovery that he requested a sphere and a cylinder to be carved onto his tombstone.

Properties and Types

  • Right Circular Cylinder: The bases are circles and are perpendicular to the axis of the cylinder (like a standard soup can).
  • Oblique Cylinder: The sides lean over, meaning the bases are not aligned directly over each other.

Cylinders are crucial in engineering. The pistons in a car engine move inside cylinders, generating the power to move the vehicle.

[Image of engine cylinder and piston]

Questions & Answers

Q: Does a cylinder have vertices? A: No, a cylinder has no corners (vertices). It has 2 edges (the circular rims) and 3 faces (2 flat, 1 curved).
Q: How do you find the volume? A: Volume = π × radius² × height.