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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.

Solution:

Given:⇒Radius of pencil=7/2mm=3.5mm⇒0.35cm=rp⇒h=14cm,Radius of graphite=1/2mm=0.05cm⇒Volume of wood in pencil=π(r2p−r2g)h⇒22/7[(0.35)2−(0.05)2]14⇒22/7(0.1225−0.0025)×14⇒44×0.12=5.28cm3⇒Volume of a graphite=πr2gh⇒22/7×(0.05)2×14cm3⇒44×0.0025cm3⇒0.11cm3