Surface Area of Sphere (Formula & Solved Examples)

A sphere is defined as a three-dimensional (3-D) object. Spheres are round in shape. The sphere can also be defined in three axes, i.e., x-axis, y-axis and z-axis and a sphere does not have any edges or vertices, like any other 3D shape.

The points on the surface of the sphere are always equidistant from the centre therefore, the distance between the centre and the surface of the sphere is always equal at any point. This distance is said to be the radius of the sphere.

What is a Sphere?

The sphere is a geometrical figure that is always round in shape. The sphere is also defined as a three-dimensional (3-D) space. The sphere is three dimensional solid, which has surface area and volume, just like a circle, each point of the sphere is at an equal distance from the centre.

• Radius- Radius is defined as the distance between the surface and centre of the sphere.

• Diameter-Diameter is the distance from one point to another point on the surface of the sphere which passes through the centre.

• Surface area-The surface area is the region occupied by the surface of the sphere.

• Volume-Volume is defined as the amount of space occupied by any spherical object.

Important Facts on Sphere

• A sphere is always a symmetrical object

• All the surface points of the sphere are always equidistant from the centre.

• It has only a curved surface, no flat surface, no edges and no vertices

Shape of Sphere

The shape of a sphere is always round in shape. Sphere does not have any faces. The sphere is a geometrical three-dimensional (3-D) solid having a curved surface like other solids, such as cubes, cuboids, cones and cylinders, only a sphere does not have any flat surface or an edge.

Examples Of The Sphere

The examples of sphere is given below-

• Basketballs

• World Globe

• Marbles

• Planets

• Moon

Properties Of A Sphere

The properties of the sphere are also called attributes of the sphere, the important properties is given below-

• A sphere is a symmetrical object.

• It is not a polyhedron

• All the points on the surface of the sphere are equidistant from the centre to each other

• Only the sphere does not have any surface of centres

• It has constant mean curvature

• A sphere has a constant width and circumference also.

Equation Of A Sphere

In analytical geometry, let us consider “r” is the radius, (x, y, z) is the locus of all points and \lgroup\:x_{o},y_{o},z_{o}\rgroup is the centre of a sphere, then the equation of a sphere will be given by:

\lgroup\:x-x_{o}\rgroup^{2}+\lgroup\:y-y_{o}\rgroup^{2}+\lgroup\:z-z_{o}\rgroup^{2}=r^{2}

Sphere Formulas

The common formulas of the sphere are:

• The surface area of a sphere, SA = 4\Pi\:r^{2}unit^{2}

• Volume of sphere, V = \frac{4}{3}\Pi\:r^{3}unit^{3}

• Diameter of sphere, D = 2r, where r is the radius

Surface Area Of A Sphere

The surface area of a sphere is defined as the total area covered by the surface of a sphere in a three-dimensional space. The formula of the surface is given by:

• The Surface Area of a Sphere(SA) = 4\Pi\:r^{2}unit^{2}

Here r = radius of the sphere.

How To Find The Area Of A Sphere?

To find the area of the sphere following steps are given below-

• Firstly find the radius of the given sphere

• Then mention the value of radius in the surface area formula, i.e. (4πr²)

• And at last solve the expression and evaluate the final value

Area Of Hemisphere

Hemisphere is a three-dimensional (3d) shape, which is just half of the sphere. When a plane cuts the sphere in two equal halves then we obtain the hemisphere.

The TSA stands for the total surface area of the hemisphere is equal to the sum of its curved surface area and the base area also called a circular base.

TSA of hemisphere = Half of the area of sphere + Base area

TSA = 2\Pi\:r^{2}+\Pi\:r^{2}

TSA = 3\Pi\:r^{2}

Volume of Sphere

The volume of the sphere is defined as the number of cubic units which is needed to fill any sphere.

The formula for the volume of the sphere is given below-

• Volume = \frac{4}{3}\Pi\:r^{3}unit^{3}

S.I unit of the sphere is given by cubic meters (m^{3} )

The derivation is given as:

Let us say V is the volume of the Sphere

= \frac{1}{3}A_{1}r+\frac{1}{3}A_{2}r+\frac{1}{3}A_{3}r+\dotso\frac{1}{3}A_{n}r (Sum of the volumes of all pyramids)

= 1/3(Surface area of the sphere) r

=\frac{1}{3}\lgroup4\Pi\:r^{2}\rgroup\times\:r

=\frac{4}{3}\lgroup\Pi\:r^{3}\rgroup

How To Find The Volume Of A Sphere?

Steps for Finding the Volume of a Sphere are given below-

Step 1: The first step is to find the radius of a sphere and cubic it.

Step 2: And then take the product of \frac{4}{3}\Pi and then cube the radius of the given sphere.

Step 3: And lastly, write the answer in the unit of measurement.