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Volume of a Cylinder

A cylinder is not a prism, since not all its edges are straight lines. However, cylinders are like cross section of a cylinderprisms in that they have a uniform cross-section, the only difference being a cylinder has a curved surface.

A cylinder has two end faces and its cross-section is identical to either of its faces. Its height, h, is measured at right angles to the base of the cylinder.

The volume of a cylinder is equal to the area of the base multiplied by its height. The base of the cylinder is a circle, so area of its base is given by the area of a circle, viz. A = pi r^2.

So the volume of a cylinder, V is given by the formula –

V  =  pi r^2 h


Now let us look at a few examples to calculate the volume of a cylinder.

Find the volumes of the following cylinders, correct to 1 decimal place.

1.  V  =  pi r^2 h  volume of a cylinder_1

=  pi~*~7^2~*~15

=  22~*~7~*~15

=  2310 cm3


2.  V  =  pi r^2 h          volume of a cylinder_2

=  pi~*~3^2~*~12

=  3.14~*~9~*~12

=  339.10 cm3


3.  This shape is half of a cylinder. Hence its volume will be     volume of half cylinder

V  =  1/2 pi r^2 h

=  1/2~*~pi~*~2.3^2~*~20  (since r = 2.3 mm)

=  10~*~3.14~*~2.3^2

=  166.2 mm3