What is the formula for the volume of a sphere?
A sphere is a three-dimensional solid figure in which a set of points are connected with one common point at equal distances.
Answer: The formula for the volume of a sphere is: (a) Volume of Solid Sphere = (4/3)πr3, (b) Volume of a Hollow Sphere = (4/3)π(R3 - r3).
Let's look into the steps
The volume of a sphere is the measure of space that can be occupied by a sphere.
The formula of volume of a sphere can be given for a solid as well as a hollow sphere.
In the case of a solid sphere, we only have one radius but in the case of a hollow sphere, there are two radii, having two different values of radius one for the outer sphere and one for the inner sphere.
Let's look into both the formulas shown below.
The volume of Solid Sphere:
V = (4/3)πr3
The volume of Hollow Sphere:
If the radius of the outer sphere is R, the radius of the inner sphere is r and the volume of the sphere is V.
Then, the volume of the sphere is given by:
V = Volume of Outer Sphere - Volume of Inner Sphere
V = (4/3)πR3 - (4/3)πr3 = (4/3)π(R3 - r3)
Let's take an example to understand this. We will find the volume of a sphere having a radius of 8 inches.
As we know, the volume of a sphere, V = (4/3)πr3
Here, r = 8 inches
Thus, volume of sphere, V = (4/3)πr3 = ((4/3) × π × 83) in3
⇒ V = 2145.52 in3
Thus, the volume of the sphere is 2145.52 in3.
We can also use Cuemath's online volume of a sphere calculator to calculate the volume of a given sphere.