A lead pencil consist of a cylinder of wood with a solid cylinder of graphite filled in the interior. the diameter of the pencil is 8mm and the diameter of graphite is 2mm . if the length of the pencil is 21cm .find the volume of wood and that of the graphite.
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Here, h = 14 cm.
Radius of the pencil (R) = 7/ 2 mm = 0.35 cm.
Radius of the graphite (r) = 1/ 2 mm = 0.05 cm.
Volume of the the graphite = π r2h
= 22/ 7 × 0.05 × 0.05 × 14 cm³ = 0.11 cm³
Volume of the the wood = π (R2 – r2)h
= 22/ 7 × [(0.35)2 – (0.05)2] × 14 cm3
= 22/ 7 × 0.4 × 0.3 × 14 cm3 = 5.28 cm³
Hence, volume of the wood = 5.28 cm³ and volume of the graphite
= 0.11 cm³
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