What is Sphere? Sphere Formula – Surface Area & Volume of a Sphere

What is Sphere?

You must have seen students playing with footballs, tennis balls, table tennis etc. These all are the examples of Sphere in 3-dimensional geometry. When a semi-circle is rotated across its diameters then it will become a Sphere. The radius of Sphere would be equal to the radius of a semi-circle.

A Sphere is the locus of points in space that moves in such a way that its distance from a fixed point always remains constant. The fixed distance is measured as radius and the fixed point is measured as the center of the Sphere. You must be wondering what the difference between a Circle and the Sphere is. The circle is a two-dimensional figure and the Sphere is a 3-dimensional figure in the plane. If the length of the radius is made twice then it is converted to the diameter of the Sphere.

Sphere Formula

This is easy to calculate the surface area or volume of a Sphere if you know the measurements especially radius. You just need to put values into Formulas and calculate the final outcome. If a Sphere is cut into halves then it becomes a hemisphere with the same radius and center point. Here, are some of the popular properties of a Sphere and they are given below –

  • This is a perfectly symmetrical shape where all points are equidistant from the center.
  • There is no edges or vertices in case of a Sphere.
  • It has one surface not flat.
  • This is not a polyhedron.

\[\large Diameter\;of\;a\;sphere=2r\]

\[\large Circumference\;of\;a\;sphere=2\pi r\]

\[\large Surface\;area\;of\;a\;sphere=4\pi r^{2}\]

\[\large Volume\;of\;a\;sphere=\frac{4}{3}\: \pi r^{3}\]

Surface Area of a Sphere Formula

In our daily life, we deal with a variety of Spheres like basketballs, tennis balls, footballs etc. In other words, we can say that Sphere is the common shaped that is frequently used by the Sports world. All balls are of Sphere shape but having different radii. This is easy to calculate the surface area or volume of a Sphere if you know the radius of Spherical objects. In mathematics, the surface area of a Sphere formula is given as –

\[\large Surface\;area\;of\;a\;sphere=4\pi r^{2}\]

Where r is the fixed distance from the center point or we can call it the radius of Sphere.

The Volume of a Sphere Formula

With a list of complete Sphere Formulas, this is easy to calculate the surface area, curved surface area, and the volume of the Sphere. You just have to put the values in formula and solve any typical mathematics problem. This is important to learn Cylinder Formulas during your school days because they are frequently used in day-to-day life too. Also, they are helpful in preparing yourself for competitive exams.

Here, in this section, we will focus on the fact of how to calculate the volume of a Sphere. Volume in general terms can be defined as the total capacity of a 3D object. In the same way, the volume of a Sphere is nothing but the space occupied by it within boundaries. In mathematics, the volume of a Sphere Formula can be written as –

\[\large Volume\;of\;a\;sphere=\frac{4}{3}\: \pi r^{3}\]

Where r is the fixed distance from the center point or we can call it the radius of Sphere.

Question: Calculate the diameter, circumference, surface area and volume of a sphere of radius 9 cm ?

Solution:

Given,
r = 7 cm

Diameter of a sphere
=2r
= 2 × 9
=18 cm

Circumference of a sphere

= 2πr
= 2 × π × 9
= 56.54 cm

Surface area of a sphere

\[\large 4\pi r^{2}\]
\[\large 4\times \pi \times 9^{2}\]
\[\large 4\times \pi \times 81\]
= 1017.87 cm

Volume of a sphere

\[\large \frac{4}{3}\;\pi r^{3}\]
\[\large \frac{4}{3}\;\pi 9^{3}\]
= 338.2722 cm


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