# Sphere

## Sphere Definition

A sphere is an object that is an absolutely round geometrical shape in three-dimensional space. In this article, let us look at the sphere definition, properties and sphere formulas like surface area and volume of a sphere along with examples in detail.

Like a circle in 2D space, a **sphere** is a three-dimensional shape and it is mathematically defined as a set of points from the given point called “centre” with an equal distance called radius “r” in the three-dimensional space or Euclidean space. The diameter “d’ is twice the radius. The pair of points that connects the opposite sides of a sphere is called “antipodes”. The sphere is sometimes interchangeably called “ball”.

You will study the following important topics about **Sphere:**

- Equation
- Properties
- Formula
- Surface Area
- Volume
- Examples

## Equation of a Sphere

In analytical geometry, the sphere with radius “r”, the locus of all the points (x, y, z) and centre (x_{0}, y_{0}, z_{0}), then the equation of a sphere is given as

**(x -x _{0})^{2} + (y – y_{0})^{2} + (z-z_{0})^{2} = r^{2}**

## Properties of a sphere

The important properties of the sphere are:

- A sphere is perfectly symmetrical
- It is not a polyhedron
- All the points on the surface are equidistant from the centre.
- It does not have a surface of centres
- It has constant mean curvature
- It has a constant width and circumference.

## Sphere Formula

We know that the radius is twice the radius, the diameter of a sphere formula is given as:

The diameter of a sphere,** D = 2r units**

Since all the three-dimensional objects have the surface area and volume, the surface area and the volume of the sphere is explained here.

### Surface Area of a Sphere

The surface area of a sphere is the total area of the surface of a sphere, then the formula is written as,

**The Surface Area of a Sphere(SA) = 4πr ^{2} Square units**

Where “r” is the radius of the sphere.

### Volume of a Sphere

The amount of space occupied by the object three-dimensional object called a sphere is known as the volume of the sphere. According to the Archimedes Principle, the volume of a sphere is given as,

**The volume of Sphere(V) = 4/3 πr ^{3} Cubic Units**

### Sphere Examples

**Example 1:**

Find the volume of the sphere that has a diameter of 10 cm?

**Solution:**

Given, Diameter, d = 10 cm

We know that D = 2 r units

Therefore, the radius of a sphere, r = d / 2 = 10 / 2 = 5 cm

To find the volume:

The **volume of sphere = 4/3 πr ^{3} Cubic Units**

V = (4/3)× (22/7) ×5^{3}

Therefore, the volume of sphere, V = 522 cubic units

**Example 2:**

Determine the surface area of a sphere having a radius of 7 cm

**Solution:**

Given radius = 7 cm

**The Surface Area of a Sphere(SA) = 4πr ^{2} Square units**

SA = 4× (22/7)× 7^{2}

SA = 4 × 22 × 7

SA = 616 cm^{2}

Therefore, the surface area of a sphere = 616 square units.