Geometry - Sphere

Sphere

Understanding the Sphere: Definition, Properties, and Key Formulas

A sphere is a perfectly round three-dimensional geometric shape. Every point on the surface of a sphere is equidistant from its center. It’s the 3D analogue of a circle and is widely used in geometry, physics, and engineering.

Sphere

Key Properties of a Sphere

  • Perfectly symmetrical 3D object
  • No edges or vertices
  • All points on the surface are at a constant radius \(r\) from the center

Key Formulas

1. Surface Area \(A\):

\[ A = 4 \pi r^2 \]

  • \(r\): Radius of the sphere
  • \(\pi \approx 3.1416\)

2. Volume \(V\):

\[ V = \frac{4}{3} \pi r^3 \]

3. Diameter \(d\):

\[ d = 2r \]

Applications of Spheres

  • Physics: Models for planets, atoms, and bubbles
  • Sports: Balls (football, basketball) are spherical
  • Engineering: Bearings and domes use spherical design
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