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Question

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 and that of the graphite.
[Assume π=227]

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Solution


Radius (r1) of the pencil =(72) mm=(0.72 cm=0.35 cm)(10 mm=1 cm)

Radius (r2) of the graphite =(12)mm=(0.12)cm=0.05 cm

Height (h) of the pencil = 14 cm

Volume of wood in the pencil
=π(r21r22)h
=[227{((0.35)2(0.05))2×14}]cm3
=[227(0.12250.0025)×14]cm3
=(44×0.12)cm3
=5.28 cm3

Volume of the graphite
=πr22h=[227×(0.05)2×14]cm3
=(44×0.0025)cm3
=0.11 cm3


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