A sphere is a perfectly round geometrical object with all points on the surface laying the same distance 'r' from the center point. The amount of space occupied by the object is called volume. It unit of measurement is cubic units. Since every real object occupies some space. It is usually specified by its three dimensions-length, breadth and height. In case of circular, cylindrical and spherical object the specifying object may change to radius, angles etc.

Sphere is a three-dimensional object shaped like a ball. Every point on the surface is the same distance from the center. The volume of the sphere is equal to the product of $\frac{4}{3}$$\pi$ and the cube of the radius of the sphere. It unit of measurement is m3, cm3, inches3 etc. The formula for the volume of a sphere involves cubing the radius.

Sphere

The volume of a sphere can be found by the formula:

Volume = $\frac{4}{3}$$\pi r^3$

Where 'r' is the radius of the sphere.

A sphere is a solid figure bounded by a curved surface such that every point on the surface is the same distance from the center. To find the volume of the sphere firstly, find the radius of the sphere and cubic it. Secondly apply the formula of the volume of the sphere.

Steps for Finding the Volume of a Sphere:

Step 1:
Find the radius of a sphere and cubic it.

Step 2: Take the product of $\frac{4}{3}$$\pi$ and the cube of the radius of the sphere.

Step 3: Write answer in the proper cubic unit of measurement.


Let us see with the help of examples, how to find the volume of the sphere:

Example 1:
Find the volume of a sphere of diameter 12 m, rounding your answer to two decimal places.(using $\pi$ = 3.14).

Solution:
Given
Diameter of the sphere (d) = 12 m

Step 1:

Find the radius of the sphere:

Radius of the sphere (r) = $\frac{d}{2} = \frac{12}{2}$ = 6 m

Step 2:

Volume of the sphere (V) = $\frac{4}{3}$$\pi r^3$

=> V = $\frac{4}{3}$ * 3. 14 * 63

=> V = $\frac{4}{3}$ * 3.14 * 6 * 6 * 6

= $\frac{4}{3}$ * 3.14 * 216

= 904.32

Hence the volume of the sphere is 904.32 m3 .

Example 2:

A plane passes through the center of a sphere and forms a circle with a radius of 12 feet. What is the volume of the sphere.

Solution:

Given
Radius of the sphere = 12 feet

Volume of the sphere (V) = $\frac{4}{3}$$\pi r^3$

= $\frac{4}{3}$ * 3.14 * 123

= $\frac{4}{3}$ * 3.14 * 12 * 12 * 12

= 7234.56

Hence volume of the sphere is 7234.56 feet3 .