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Definition of Volume:

  • Volume is the amount of three-dimensional space encased by a closed surface, for instance, the space that a substance (strong, fluid, gas, or plasma) or shape involves or contains. 
  • Volume is frequently measured numerically utilizing the SI derived unit, the cubic meter. 
  • The volume of a container is by and large comprehended to be the limit of the compartment, i. e. the measure of liquid (gas or fluid) that the compartment could hold, instead of the measure of space the holder itself dislodges.

Explanation of Volume:

  • Three dimensional scientific shapes are additionally allotted volumes. Volumes of some basic shapes, for example, normal, straight-edged, and roundabout shapes can be effortlessly computed utilizing number-crunching equations. 
  • Volumes of an entangled shape can be figured by indispensable math if a recipe exists for the shape's limit. 
  • Where a fluctuation fit as a fiddle and volume happens, for example, those that exist between various individuals, these can be computed utilizing three-dimensional systems, for example, the Body Volume Index. One-dimensional figures, (for example, lines) and two-dimensional shapes, (for example, squares) are appointed zero volume in the three-dimensional space.

Volume of a Sphere:
 The formula for volume of a sphere is   π .

Example #1

Find Vsphere   if r = 2 inches

Vsphere = 4/3 × pi × r^3

Vsphere = 4/3 × 3.14 × 23

Vsphere = 4/3 × 3.14 × 8

Vsphere = 4/3 × 25.12

Vsphere = 4/3 × 25.12/1 

Vsphere = (4 × 25.12)/(3 × 1) 

Vsphere = (100.48)/3 

Vsphere = 33.49 inches^3

Example #2

Find Vsphere   if r = 3 cm 

Vsphere = 4/3 × pi × r^3

Vsphere = 4/3 × 3.14 × 33

Vsphere = 4/3 × 3.14 × 27

Vsphere = 4/3 × 84.78

Vsphere = 4/3 × 84.78/1 

Vsphere = (4 × 84.78)/(3 × 1) 

Vsphere = (339.12)/3 

Vsphere = 113.04 cm^3

Volume of a Cone:
   The volume of a cone can be find by using formula π

Example #1:

Calculate the volume if r = 2 cm and h = 3 cm

Vcone = 1/3 × 3.14 × 22 × 3

Vcone = 1/3 × 3.14 × 4 × 3

Vcone = 1/3 × 3.14 × 12

Vcone = 1/3 × 37.68 

Vcone = 1/3 × 37.68/1

Vcone = (1 × 37.68)/(3 × 1)

Vcone = 37.68/3 

Vcone = 12.56 cm^3

Example #2:

Calculate the volume if r = 4 cm and h = 2 cm

Vcone = 1/3 × 3.14 × 42 × 2

Vcone = 1/3 × 3.14 × 16 × 2

Vcone = 1/3 × 3.14 × 32

Vcone = 1/3 × 100.48 

Vcone = 1/3 × 100.48/1

Vcone = (1 × 100.48)/(3 × 1)

Vcone = 100.48/3 

Vcone = 33.49 cm^3

Volume of a Cube:
   The formula for finding the volume of a cube is Vcube = a3 = a × a × a.

Example #1:

Find the volume if the length of one side is 2 cm

Vcube = 23

Vcube = 2 × 2 × 2

Vcube = 8 cm^3

Example #2:

Find the volume if the length of one side is 3 cm

Vcube = 33

Vcube = 3 × 3 × 3

Vcube = 27 cm^3

Example #3:

Find the volume if the length of one side is 3/2 cm

Vcube = (3/2)^3

Vcube = 3/2 × 3/2 × 3/2

Vcube = (3 × 3 × 3)/(2 × 2 × 2) Vcube = 27/8 Vcube = 3.375 cm^3

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