The length of outer and innner diameter of a hollow right circular cylinder are 16 cm and 12 cm respectively and height of cylinder is 36 cm. how many solid cylinders of 2 cm radius and 6 cm length may be obtained by melting this cylinder.

Explanation

The outer diameter = 16 cm
`:.` The outer radius `= (16)/(2) cm = 8 cm`
The inner diameter = 12 cm
`:.` the inner radius `= (12)/(2) cm = 6 cm` .
Height of the cylinder `= 36 cm`.
So, the volume of the materials of the hollow cylinder
`= (22)/(7) {(8)^(2) - (6)^(2)}xx36 c c = (22)/(7) xx 28 xx 36 c c = 3168 c c `.
The radius of small cylinders to be made `= 2 cm` and their lengths = 6 cm each.
`:.` The volume of each small cylinders to be made `= (22)/(7) xx (2)^(2) xx 6 c c = (22)/(7) xx 4 xx 6 c c`
So the required number of small cylinders `= ((22)/(7)xx28xx36)/((22)/(7)xx4xx6)=42`.
Hence the required number of cylinders to be made is equal to 42.
[ N.B. : If the outer and inner radius ( not diameter) be 16 cm and 12 cm respectively, then the number of cylinders is 168. ]