Volume of a Sphere

Sphere is derived from the Greek word 'sphaira, which means globe or ball. A sphere is a three dimensional shape that has no base, edge, vertex or face. It is a round body that has all its points on the surface that are equidistant from the center. It is a perfectly symmetrical shape that has distance 'r' (radius) from the center. The diameter of the sphere is the maximum straight distance through the sphere that is twice the radius. You can calculate the volume of a sphere using a simple formula. Many times you may come across the question, 'what is the volume of the sphere' in your geometry problem sheets. If you are facing a similar problem then the following explanation will help you know more on how to calculate the volume of a sphere.

Volume of a Sphere - Equation Derivation
Before we can understand how to find the volume of a sphere, let us go into the details of volume of a sphere's equation derivation. This will help you understand how to calculate the volume of a sphere better. The volume of a sphere formula was derived by Archimedes. He showed that the volume of sphere is 2/3 of a circumscribed cylinder. Today, integral calculus is used to sum the volumes of an infinite number of circular disks with infinitesimal thickness. These discs have incremental volume δV as the product of cross sectional area of the disk x and thickness δx. Therefore,
δV ≈ πy² • δx

You will get the total volume by summation of all the incremental volumes by:
V ≈ ∑πy² • δx

When the δx approaches zero in the limit, the equation becomes:

V = _{x = 0}∫^{x = r} πy² • dx

A right angled triangle at any given x will connect x, y and r to the origin. This is because it will follow the Pythagorean theorem as follows:

r² = x² + y²

Thus, when you substitute y with the function of x you get:

V = _{x = 0}∫^{x = r} π (r² - x²) dx

Therefore,

V = π ( r³ - r³/ 3) = 2/3 πr³

Therefore, the volume of the sphere equation thus derived is as follows:

V = 4/3 πr³

You can use this formula to solve your query on how to find volume of a sphere. Let me explain the use of volume of a sphere formula with the following example.

Example
Find the volume of a sphere with a radius 7.6 m and round your answer to two decimal places.

Answer
V   = 4/3 πr³
    = 4/3 x 3.14159 x 7.6³
    = 4/3 x 3.14159 x 438.976
V   = 1838.7 m³

Volume of a Sphere Formula using Diameter
The above volume of a sphere formula was calculated using radius of the sphere. Volume is a three dimensional amount of space that is occupied by an object. In a sphere, the distance from one point on the surface to another point on the surface through the center is measured with the help of diameter. To find volume of a sphere formula using diameter, follow the equation below.

In a sphere the volume V is equal to 3.14159 (pi) times the diameter d that is cubed by 6. Therefore, the volume of a sphere formula in terms of diameter can also be written in the following way, as diameter is twice the radius (r).

V = (π • d^ 3)/6

This is all about how to calculate the volume of a sphere using the radius and diameter of the sphere. You just need to remember the formula and put in the values you've got. I hope this article on how to find the volume of a sphere has proved to be useful to all you who are zapped with mathematics.