Volume Of A Sphere Formula

What Is A Sphere?

The sphere is one of the most interesting shapes found in nature, from the blow bubbles to the planets. Knowing its volume is very important to us because we use it in such domains as physics, engineering, and even art. In this article, we shall discuss the volume of a sphere, its computation, and its application in reality.

A sphere is a three-dimensional rounded object characterized by the property that every point on its surface is equidistant from its center. The distance is called the radius.

Formula For Volume Of A Sphere

The volume V of a sphere is given by the formula:

Where,

• V = Volume of the sphere

•  r = Radius of the sphere

• π(pi) ≈ 3.14159

Volume of a Sphere Derivation

The volume of a sphere can be alternatively interpreted as the number of cubic units that fill up the sphere.

Assume a sphere of radius, r cut into pyramids. Then, we can easily interpret that the volume of the sphere is equal to the total volume of all those pyramids having height, r and having a sum of base area being equal to the surface area of the sphere as represented in the figure.

The total volume is obtained by adding up the volume of all the pyramids.

The volume of the sphere = Sum of volumes of all pyramids

The volume of the sphere=

Volume of the sphere= 

Real world Applications

• Science and Engineering: Calculations involving the volume of spheres find major application areas in disciplines like physics where such calculations can be involved in determining buoyancy and pressure.

• Architecture: Spherical forms are used in designing domes and other constructs in architecture, both for aesthetic and structural functions.

• Sports: Most sports balls, such as basketballs and soccer balls, are spherically shaped. It is valuable to calculate this volume for the use of materials and in its design.

• Medicine: In medical imaging and dosimetry, spheres represent body organs and dosages.

Solved Problems Using Formula of Volume of Sphere

Problem 1: Determine the volume of the sphere which has a radius of 11 feet.

Solution:

Given, 

Radius of sphere,

 r = 11 feet 

So, Volume of a sphere is given by, 

Problem 2: Determine the radius of a spherical ball, whose volume is

Solution:

Given

Volume of sphere= 

The ball has a radius of about 4.34 cm.

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