Volume of Geometric Solids

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies or contains, often quantified numerically using the SI derived unit,  the cubic meter.The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.(Source:Wikipedia)
                                                                                                                                                     

Volume of cube:

Volume of cube

The volume of cube can be determined by finding the cube of its side.
                                                                                                     
                                                                                                  A Typical Square
                                                                        Formula: Volume of cube = a³  cubic units
Example for volume of geometric solids Cube :
1. Find the volume of the cube of side 10cm
Let, a = 10cm
Formula: a³                                                                                                            
Solution:
Volume of the cube = 10 x 10 x 10
                                = 1000 cm³
Example for volume of geometric solids Cube 2:
2.Find the volume of the cube of side 25m
Let, a = 25m
Formula: a³
Solution:
Volume of the cube of side 25m  =  25 x 25 x 25
                                                     = 15625m³                        

Volume of rectangular prism (Cuboid)

       The volume of cube can be determined by multiplying its sides a, b, and c

                                         

                                      Rectangle prism

Formula:   Volume of the rectangular prism = a x b x c cubic units

Example for volume of geometric solids Rectangular prism :

3.Find the volume of the rectangular prism of sides 10cm, 15cm, 25cm.

Let, a=10cm, b=15cm,  c=25cm

Formula used: a x b x c

Solution:

Volume of the rectangular prism = 10 x 15 x 25

                                                        = 3750 m³

Volume of sphere:

      

                                                      

The volume of sphere can be determined by using the formula `4/3 ` `pi ` r³

Example for volume of geometric solids Sphere : 

4.Find the volume of the sphere of radius 3cm

Let, radius r of the sphere = 3cm

Formula: ` 4/3`` pi` r³

Solution:Volume of the sphere =` 4/3 xx 22 /7xx 3^3`

                                                     = 113.14cm³

Practice Problems

1.     Find the volume of the cube of side 65cm.

2.     Find the volume of the sphere of radius 7m.

       3.     Find the volume of the cuboid of side 2m, 5m, and 6m.

Solution to Practice Problems:

1.  274625 cm³

2.  1437.33m³

3.  60m³