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# Sphere

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 Sub Topics In Geometry, we studied about lots of geometrical shape and figures which are formed on two dimensional planes. In the geometry some of the figures are available that are represented or formed on the three dimensional plane. A sphere is a word which comes from the Greek word 'sphaira' which refers to “globe or ball”. A sphere can be considered as a perfectly round geometrical object in the 3–D spaces. But the basic difference between the sphere and Circle is that circle is a geometrical shape which is formed on the 2–D planes. A perfect sphere is a shape which has the equal distance from the center Point of the sphere. In mathematics, a sphere can be described as a 3–D surface shape, where all the points have an equal distance from a fixed point which is known as center of the sphere. The shape of sphere has no vertices or no sides. In the standard definition we can define the sphere as the Set of all points in three dimensional Euclidean spaces, which are located at a distance 'r' form the given point (it means center of the sphere). As like the other geometrical shape, in mathematics various other formulas are provided to calculate the volume of the sphere. Below is shown you the formula of Volume of Sphere: Volume of sphere = 4 / 3 * ∏ * r3, Suppose there is a shape of sphere with the radius of 7 inches. The volume of sphere can be calculated by applying the formula of sphere. For the formula of sphere we first need the value of the radius, where radius equal to the 7 inches. After that applying the values of the pi and radius in the formula of sphere, we can easily get the area of sphere.             $\frac{4}{3}$ * $\frac{22}{7}$ * 7 3,  = 1436.02 inches3.

## Volume of Sphere

Sphere can be defined as a round 3 dimensional geometrical object; example of Sphere is ‘earth’. Just like a Circle sphere also has radius which is the distance from Centre of sphere to the surface of sphere. All points on surface of circle are at equal distance from the centre of sphere.

The formula for calculating volume of sphere was given by ‘Archimedes’. The volume of a sphere is $\frac{4}{3}$ multiplied by ∏r3 or v = $\frac{4}{3}$ ∏r3, where ‘v’ is the volume of sphere, value of ∏ = 3.14 and ‘r’ is the radius of sphere.

Volume of sphere can be measured as the total number of cubic units that exactly fill the sphere. The unit of volume of sphere is represented in cubes like inch3, m3, etc.

We can use the steps shown below for calculating volume of the sphere:

1. Use the formula for volume of sphere $\frac{4}{3}$ ∏ r3.
2. Put the value of ∏ in above formula.
3. Now find the Cube of radius and put it in the formula, if Diameter is given then we can find the radius by dividing the diameter by 2.
4. Now multiply the cube of radius by $\frac{4}{3}$ ∏ and we get the volume of sphere.

Suppose we have a football with diameter 16 inches then we can find the volume as:

1. First calculate radius by dividing diameter by 2 i.e. r = $\frac{d}{2}$ = $\frac{16}{2}$ = 8 inch.
2. Find cube of radius i.e. r3 = (8)3 = 512.
3. Put r3 in formula i.e. $\frac{4}{3}$ ∏ r3 = $\frac{4}{3}$ (3.14) (512) = 2143.57 inch3.

This is how we can find volume of a sphere.

## TSA of Sphere

A Sphere is a three dimensional object which has shape like a round object. Every Point of a sphere is at fix distance from the center of a sphere because it has round shape.

Now we will see some properties of a sphere which are given below:

1. It is a perfectly symmetrical object.
2. In a sphere no vertices and edges are present.
3. Shape of a sphere is not like polyhedron.
4. Points on the surface of a sphere are equidistance from the center of a sphere.

Now we will see the total surface area of sphere.

The formula for total surface area is given by:

Total surface area of sphere = 4 * $\pi$ * r2;

Where, ‘r’ is the radius of a sphere.

Now we will see how to find the total surface area of sphere:

We have to follow some steps for finding the total surface area of a sphere and the steps are given below:

Step 1: For finding the total surface area first we find the radius of a sphere.

Step 2: If we have radius then we can easily find the TSA of sphere by putting the radius value in the formula.
Suppose we have radius of a sphere equals to 17 inch and we have to find the total surface area of sphere.

For finding the TSA of a sphere we have to follow all the above steps:

Step 1: First we find the value of radius.

Here the radius of sphere is 17 inch.

Value of $\pi$ is 3.14

We know that the formula for TSA is:

Total surface area of sphere = 4 * $\pi$ * r2;

TSA = 4 * 3.14 * (17)2;

TSA = 4 * 3.14 * 289;

TSA = 3629.84 inch2.

## LSA of Sphere

A three dimensional object which has a shape like a round ball is known as Sphere. So by the definition of sphere we can say that every Point of a sphere is at fix distance from the center.

Some properties of a sphere is also defined which are given below.

1. Sphere is a perfectly symmetrical object.
2. No vertices and edges are present in a sphere.
3. Shape of a sphere is not follows the properties of polyhedron.
4. Points on the surface are equidistance from the center of a sphere.

Now we will see the lateral surface area of sphere.

Lateral surface area of a sphere is the sum of the surface areas of all its faces; also include the base of the Solid.
The formula for lateral surface area is given by:

Lateral surface area of sphere = 4 * $\pi$ * r2;

Where, ‘r’ is the radius of a sphere.

Now we will see how to find the lateral surface area of a sphere.

For finding the lateral surface area of a sphere we follow some of the steps which are given below:

Step 1: For finding the lateral surface area first we find the value of radius.

Step 2: If we have radius then we can easily find the LSA of sphere by putting the radius value in the formula.

Suppose radius of a sphere is 12 inch and we have to find the lateral surface area of a sphere.

Then for finding the LSA of a sphere we have to follow all the above steps:

Step 1: First we find the value of radius.

Here the radius of sphere is 12 inch.

Value of $\pi$ is 3.14,

We know that the formula for LSA is:

Lateral surface area of sphere = 4 * $\pi$ * r2;

LSA = 4 * 3.14 * (12)2;

LSA = 4 * 3.14 * 144.

LSA = 1808.64 inch2;