Why Volume of Cylinder is πr2h

Volume of Cylinder

  • Cylinder is the three-dimensional geometrical object which is having two circular bases with fixed radius which are joined by a curved surface as shown in figure.
  • The line joining the centers of two circular bases is called as the axis of cylinder.
  • And the perpendicular distance between these two centers of circular bases of cylinder is the height of the cylinder as shown in figure.
  • The space occupied by the cylinder is called as the volume of the cylinder.

Derivation for Volume of Cylinder:

  • Let us consider the cylinder with two circular bases having radius r and height h as shown in figure.
  • We know that the volume of any object is the product of base area and height of the object.
  • Here the base of cylinder is circular and the height of the cylinder is h.

  • Thus, the volume of cylinder is given by,

 

Volume of cylinder = base area*height of cylinder

 

But, the base of cylinder is circular and having radius r,

Hence, area of base = πr2

 

Now, volume of cylinder = base area * height = πr2*h

 

Thus, the volume of cylinder of base radius r and height h is given by,

Volume of cylinder = πr2*h (Hence proved.)


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