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Question

A lead pencil consists of a cylinder of wood with solid cylinder of graphite filled in the interior. The diameter of the pencil is 7mmand the diameter of the graphite is 1mm. If the length of the pencil is 14cm, find the volume of the wood and that of the graphite. (Assumeπ=227)


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Solution

Step 1: Write the given dimensions

Height of wood (and graphite) cylinderh=14cm=140mm

Radius of pencil R=72mm

Radius of graphite r=12mm

Step 2: Find the volume of the graphite

Volume of Graphite =(πr2h)

=227×12×12×140mm3=110mm3=0.11cm3

Step 3: Find the volume of the graphite

Volume of wood = Volume of pencil – Volume of graphite

=(πR2h)(πr2h)=π(R2r2)h=227722-122x140=22×20×(49/4-1/4)=22×20×12=5280mm3=52.80cm3

Hence, the volume of the wood and that of the graphite are 52.80cm3 and 0.11cm3 respectively.


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