In simple words, we can say that volume of a sphere is the correct measurement of the area
that is occupied by the sphere. A sphere is said to be a three-dimensional figure that has no
edges or vertices. Computing the volume of a sphere equation is not very difficult if students
know the formulas that are associated with it. Students need to have a good understanding of
the general or basic concepts of the sphere to get an idea for the computation of the volume of
a sphere.
The volume of Spheres: Basic Concept
This section can be very significant and helpful for you if you are facing a problem finding
the solution to “How to find the volume of a Sphere”. It is already explained or discussed that
the volume of a sphere is the correct measurement of the area that is occupied by the sphere.
A volume of a sphere is measured in units of (unit)3. Cubic centimeters or Cubic meters are
the metric units of volume, on the other hand, the USCS units come in the form of cubic feet
or cubic inches. The radius of the sphere has a great impact on its volume. A volume of a
sphere will be altered or changed with the change in its radius.
Types of Spheres
There are two types of spheres:
Solid Sphere
Hollow Sphere
You cannot opt for the same approach while computing the volume of both types of spheres.
The following sections help you to deliver thorough knowledge regarding the computation of
the volume of a sphere.
Derivation of the Volume of a Sphere
Archimedes’ Theorem states that if a cylinder, cone, and sphere all have the same cross-
sectional area and a radius of “r”, then their volume must be in the proportion of 1:2:3. If the
above-mentioned theory is accurate, then the relationship between the volumes of a cone,
cylinder, and the sphere is as follows-
The volume of cylinder= Volume of Cone+ Volume of Sphere
Therefore, you can derive that-
The volume of Sphere= Volume of Cylinder- Volume of Cone.
As you know that the volume of a cylinder is- cylinder volume= πr 2 h and the cone volume=
(1/3) πr 2 h,
The volume of a sphere = Cylinder Volume- Cone Volume.
πr 2 h- (1/3) πr 2 h= (2/3) πr 2 h
Here, cylinder height= diameter of sphere= 2r
Hence, the formula for the volume of a sphere is (2/3) πr 2 h= (2/3) πr 2 (2r) = (4/3) πr 3 .
The formula for the Volume of the Sphere
With a twist, you can compute the volume of both solids as well as hollow spheres. A hollow
sphere has two radii whereas a solid sphere has only one radius. You have two different
values of radius in the latter (one for the inner sphere and another for the outer sphere). To
make your task easy, you have to apply the formula of the radius of a sphere.
The volume of a Solid Sphere
Take the volume as “V” and the radius of the sphere formed as “r”. In this case, you can
compute the equation for the volume of a sphere with the help of the given formula:
The volume of Sphere, V= (4/3) πr 3 .
The volume of the Hollow Sphere
Take the radius of the inner sphere is “r”, the radius of the outer sphere to be “R” and the
sphere’s volume is V, then the volume of sphere is given by:
Volume of Sphere, V= Volume of Outer Sphere- Volume of Inner Sphere= (4/3) πR 3 – (4/3)
πr 3 = (4/3) π (R 3 – r 3 ).
Steps Involved In Calculating The Volume Of A Sphere
Step 1: Look for the radius value of the sphere.
Step 2: Take the radius cube
Step 3: Multiply r 3 by (4/3) π
Step 4: at the end, add all the units to get the final answer.