Some other Equations of Sphere

Equation of a sphere in vector form: “(r – r₀)² = R²”, where “r” represents a general point on the sphere’s surface, “r₀” denotes the center of the sphere, and “R” is the radius.

Equation of a sphere in cylindrical coordinates: “r² + (z – z₀)² = R²”, where “r” is the radial distance from the z-axis, “z” is the vertical distance, and “z₀” is the vertical position of the center of the sphere.

Equation of a sphere in spherical coordinates: “R = R₀”, where “R” is the distance from the origin to any point on the sphere’s surface, and “R₀” is the radius of the sphere.

Surface Area Equation of Sphere

The surface area (A) of a sphere with radius (r) is given by the formula:

Area = 4πr²

This formula calculates the total area of the sphere’s surface, which is covered by points equidistant from its center. The surface area of a sphere is a fundamental quantity used in various mathematical and physical contexts, such as in geometry, physics, and engineering.

Volume Equation of Sphere

The volume (V) of a sphere with radius (r) is given by the formula:

Volume = (4/3)πr³

This formula represents the total amount of space enclosed by the sphere. It’s derived by multiplying the volume of a sphere (4/3)πr³, where r is the radius. This volume formula is fundamental in various mathematical and physical contexts, such as in geometry, physics, and engineering.

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Sphere
Surface Area of Sphere
Volume of Area of Sphere
Mensuration

Equation of a Sphere

The equation of a sphere defines all points equidistant from its center, given by (x – h)² + (y – k)² + (z – l)² = r², where (h, k, l) is the center and r is the radius. This article provides an in-depth exploration of the equation of a sphere, its properties, applications, and related concepts.

Table of Content

What is Sphere?
Equation of Sphere

General Equation of Sphere
Parametric Equations of a Sphere
Geometrical Interpretation of the Equation of a Sphere