In simple words, the volume of a sphere is the exact measurement of the area it can occupy. A sphere is a three-dimensional figure with no edges or vertices. Finding the volume of a sphere equation isn’t difficult if you are aware of the formulas associated with it. Also, you need to have a concrete understanding of the basic concepts to get an idea.
Concept of the Volume of Spheres
If you struggle to come up with the answer to the question ‘how to find the volume of the sphere’, this section can be of great help to you. As mentioned above, the volume of a sphere is a calculation of the space that a sphere can take up. The volume unit of a sphere is the (unit)3. Cubic meters or cubic centimeters are the metric units of volume, while the USCS units come in the form of cubic inches or cubic feet. The sphere’s volume is hugely dependent on its radius. If you change the radius of a sphere, its volume will also change significantly.
Types of Spheres
There are two types of spheres:
- Solid sphere
- Hollow sphere
You can’t take the same approach while calculating the volume of both sphere types. The following sections will delve deeper into this aspect.
Derivation of the Volume of a Sphere
According to Archimedes theorem, if the radius of the cone, cylinder, and the sphere is “r” with the same cross-sectional area, it can be assumed that their volumes are in the ratio of 1:2:3. Considering the truthfulness of the above concept, the linkage between the volume of a cone, volume of a sphere, and volume of a cylinder is given as:
The volume of cylinder= Volume of Cone+ Volume of Sphere.
Henceforth, you can derive that: Volume of Sphere= Volume of Cylinder- Volume of Cone.
As you know, the cylinder volume= πr2h and the cone volume= (1/3) πr2h,
The sphere volume= Cylinder Volume- Cone Volume.
πr2h- (1/3) πr2h= (2/3) πr2h
Here, cylinder height= diameter of sphere= 2r
Therefore, sphere volume formula is (2/3) πr2h= (2/3) πr2(2r)= (4/3) πr3.
Volume of Sphere Formula
You can find the volume of both solid and hollow spheres with a twist. When it comes to the solid sphere, you have one radius, but in the case of a hollow sphere, there are two radii. In the latter, you have two different radius values (one for the inner sphere and one for the outer sphere). Here, you need to apply the radius of a sphere formula to simplify your task.
Consider the radius of the sphere formed is “r” and the volume is “V”. In this case, you can calculate the equation for the volume of a sphere by the given formula:
The volume of Sphere, V= (4/3) πr3.
- Volume of a hollow sphere
If you consider the radius of the outer sphere to be “R”, the radius of the inner sphere is “r”, and the sphere’s volume is V, then the sphere’s volume is given by:
Volume of Sphere, V= Volume of Outer Sphere- Volume of Inner Sphere= (4/3) πR3- (4/3) πr3 = (4/3) π (R3 - r3).
Steps Involved in Calculating the Volume of a Sphere
As stated above, the space within a sphere largely determines its volume, the steps to calculate the volume of a sphere equation are listed below:
Step 1: Look for the radius value of the sphere.
Step 2: Take the radius cube
Step 3: Multiply r3 by (4/3) π
Step 4: Lastly, add all the units to arrive at a final answer.
Let’s have a look at some examples to get a clear idea:
- Calculate the sphere’s volume with 4 inches radius.
As we know, the volume of sphere, V= (4/3) πr3 with r= 4 inches
V= ((4/3) × π × 43) in3
V= 268.08 in3
- Calculate the volume of the sphere whose diameter is 10 cm.
If diameter= 10 cm, radius will be= (10/2) cm= 5 cm.
Now, put this value in the sphere volume formula:
V = 4/3 π 53
V = 4/3 x 22/7 x 5 x 5 x 5
V = 4/3 x 22/7 x 125
V = 523.8 cm3
So, now that you have understood how to find the volume of a sphere, the calculations will be easier for you. All that you need is to be acquainted with the formula. Go through the above blog to get an overall idea of this intricate yet simplistic subject.
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