A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, find the volume of the wood

Explanation

Diameter of the graphite cylinder `= 1mm = (1)/(10)cm " " (because 1mm=(1)/(10)cm)`
`rArr` radius, `r = (1)/(2)cm`
Length of the graphite cylinder `= pi r^(2)h=((22)/(7)xx(1)/(20)xx(1)/(20)xx14)cm^(3)=0.11 cm^(3)`
Also, diameter of the pencil `= 7 mm = (7)/(10)cm`
`therefore` Radius of the pencil, `r=(7)/(20)cm`
and length of the pencil, h = 14 cm
`therefore` Volume of the pencil `= pi r^(2)h=((22)/(7)xx(7)/(20)xx(7)/(20)xx14)cm^(3)=5.39 cm^(3)`
Hence, volume of wood = volume of the pencil - volume of the graphite
`= (5.39-0.11)cm^(3)`
`= 5.28 cm^(3)`