What is the formula for the volume of a sphere?

Solution:

A sphere is a three-dimensional solid figure that is round in shape.

The volume of a sphere is the measure of space that can be occupied by a 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, one radius for the outer sphere and one for the inner sphere.

The volume of a solid sphere:

If the radius of the sphere is r and the volume of the sphere is V. Then, the volume of the sphere is given by:

V = (4/3)πr³

The volume of a 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, π = 22/7

Thus, volume of sphere, V = (4/3)πr³ = ((4/3) × π × 8³) = (4/3) × (22/7) × 8³

⇒ V = 2145.52 in³

Thus, the volume of the sphere is 2145.52 in³.

Hence, there are two different formulas for the volume of a sphere. (a) Volume of a solid sphere = (4/3)πr³, (b) Volume of a hollow sphere = (4/3)π(R³ - r³).

What is the formula for the volume of a sphere?

Summary:

There are two different formulas for the volume of a sphere. (a) Volume of a solid sphere = (4/3)πr³, (b) Volume of a hollow sphere = (4/3)π(R³ - r³).