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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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(i) Diameter of the graphite cylinder = 1mm `= (1)/(10) cm`
Radius of the graphite cylinder `= ((1)/(2) xx (1)/(10)) cm = (1)/(20) cm`
Length of the graphite cylinder = 14 cm
Volume of the graphite cylinder
`= (pi r^(2)h) cm^(3) = ((22)/(7) xx (1)/(20) xx (1)/(20) xx 14) cm^(3)`
`= (11)/(100) cm^(3) = 0.11 cm^(3)`
(ii) Diameter of the pencil = 7mm = `(7)/(10) cm`
Radius of the pencil `= ((1)/(2) xx (7)/(10)) cm = (7)/(20) cm`
Length of the pencil = 14 cm
Volume of the pencil
`= (pi R^(2) h) cm^(3) = ((22)/(7) xx (7)/(20) xx (7)/(20) xx 14) cm^(3)`
`= (539)/(100) cm^(3) = 5.39 cm^(3)`
`:.` volume of wood in the pencil
= (volume of the pencil) - (volume of graphite)
`= (5.39 - 0.11) cm^(3) = 5.28 cm^(3)`
(iii) Weight of the pencil
= (volume of wood) `xx` (specifc gravity of wood) + (volume of graphite) `xx` (specific gravity of graphite)
`= (5.28xx 0.7)g + (0.11 xx 2.1)g`
`= (3.696 + 0.231)g = 3.927g`

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