# 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 diam

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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

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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)