 # Sphere

In geometry, a sphere is a solid, that is absolutely round in shape defined in three-dimensional space (XYZ space). Mathematically, a sphere is defined as the set of points that is at equal distances from a common point in three dimensional space. This constant distance is called radius of sphere and the common point is the center of sphere. An example of sphere in real life is a ball. In the above figure, we can see, a sphere with radius ‘r’.

## Definition

As discussed in the introduction, sphere is a geometrical round shape in three dimensional space. It is three dimensional solid, that has surface area and volume. Just like a circle, each point of the sphere is at a equal distance from the center.

Unlike circle, which is a plane shape or flat shape, defined in XY plane, a sphere is defined in three dimensions, i.e. x-axis, y-axis and z-axis.

Important Facts:

• A sphere is a symmetrical object
• All the surface points of sphere are at equidistant from center
• A sphere has only curved surface, no flat surface, no edges and no vertices.

## Shape of Sphere

The shape of a sphere is round. It is a geometrical three dimensional solid having curved surface. Like other solids, such as cube, cuboid, cone and cylinder, a sphere does not have any flat surface or a vertex or an edge.

The real life examples of sphere is:

• World Globe
• Marbles
• Planets
• Moon

## Equation of a Sphere

In analytical geometry, if “r” is the radius, (x, y, z) is the locus of all points and (x0, y0, z0) is the center of a sphere, then the equation of a sphere is given by:

(x -x0)2 + (y – y0)2 + (z-z0)2 = r2

## 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.

## Formulas

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

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 covered by the surface of a sphere in a three dimensional space. The formula of surface are is given by:

The Surface Area of a Sphere(SA) = 4πr2 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 πr3 Cubic Units

## Solved 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 πr3 Cubic Units

V = (4/3)× (22/7) ×53

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:

The Surface Area of a Sphere(SA) = 4πr2 Square units

SA = 4× (22/7)× 72

SA = 4 × 22 × 7

SA = 616 cm2

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

## What is Hemisphere?

A hemisphere is exactly half of a sphere. It has a curved surface and a flat surface.

Register with BYJU’S – The Learning App to learn about other three-dimensional shapes also watch interactive videos to learn with ease.

## Frequently Asked Questions – FAQs

### What is a sphere?

A sphere is three dimensional, geometrical shape, that has all its surface points equidistant from a common point. The distance between surface and the common point is the radius and the common point is called center of sphere.

### How many sides a sphere have?

A sphere does not have any sides, since it is round shaped object. It has curved surface and not a flat surface.

### Is sphere a circle?

A circle is a two dimensional shape, that has area and perimeter only. A sphere is a three dimensional shape, that has surface area and volume.

### What are the characteristics of a sphere?

A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.

### What are the examples of sphere?

Football, Basketball, Globe, Planets, etc. are the examples of sphere.

### What is surface area and volume of sphere?

The surface area of a sphere is the total area covered by surface of a sphere in three dimension space. The formula for surface area is:
SA = 4πr^2 Square units
Volume of sphere is the space occupied by sphere in three dimension space. The formula is:
V = 4/3πr^3