Geometric Formulations for Circular & Cylindrical Solids
Circular geometry constitutes the foundation of trigonometry, mechanical engineering, fluid dynamics, and vessel design:
Core Formulas
- Circle: Area \(A = \pi r^2\), Circumference \(C = 2\pi r\).
- Cylinder: Volume \(V = \pi r^2 h\), Total Surface Area \(A = 2\pi r(r + h)\).
- Sphere: Volume \(V = \frac{4}{3}\pi r^3\), Surface Area \(A = 4\pi r^2\).
Frequently Asked Questions (FAQ)
What is Archimedes' ratio of a sphere to a cylinder?
Archimedes proved that both the volume and surface area of a sphere inscribed in a cylinder are exactly 2/3 the volume and surface area of the enclosing cylinder.