Units & Dimensions - VOLUME

Units & Dimensions - VOLUME
VOLUME OF CYLINDER
The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. It is given by the formula, , where r is the radius of the circular base and h is the height of the cylinder. The material could be a liquid quantity or any substance which can be filled in the cylinder uniformly.    

As a cylinder can be seen as a collection of multiple congruent disks stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height.    
    A cylinder is a solid composed of two congruent circles in parallel planes, their interiors, and all the line segments parallel to the segment containing the centers of both circles with endpoints on the circular regions.
    The volume V of a cylinder with radius r is the area of the base B times the height h .
            V=Bh
            \(V = \pi {r^2}h\)
SOLVED EXAMPLES
Example 1:     
Calculate volume of given cylinder having height 20 cm,base radius of 14 cm. (Take \(\pi ={22 \over 7}\))    
Solution:
    Height  = 20 cm
    radius = 14 cm
    we know that;
    Volume, \(V = \pi {r^2}h\) cubic units
    V= \(22\over 7\)×14×14×20
    V= 12320 cm³
    Therefore, the volume of a cylinder = 12320 cm³  
Example 2:    
    Calculate the radius of base of a cylindrical container of volume 440 cm3. Height of the cylindrical container is 35 cm.(Take \(\pi ={22 \over 7}\)    )
Solution:
    Volume = 440 cm³
    Height = 35 cm
    We know from the formula of cylinder;
    Volume,   cubic units
    So, 440 = \(22\over 7\)×r²×35
    r² = (440 × 7)/(22 × 35 ) = 3080/770 = 4
    Therefore, r = 2 cm
    Therefore, the radius of a cylinder = 2 cm.