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 pi=(22)/(7)]

Fiona Chung

Fiona Chung

Answered question

2023-03-27

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 = 22 7 ]

Answer & Explanation

nelagodafsed

nelagodafsed

Beginner2023-03-28Added 8 answers

Radius ( r 1 ) of the pencil = ( 7 2 ) m m = ( 0.7 2 c m = 0.35 c m ) ( 10 m m = 1 c m )
Radius ( r 2 ) of the graphite = ( 1 2 ) m m = ( 0.1 2 ) c m = 0.05 c m
Height (h) of the pencil = 14 cm
Volume of wood in the pencil
= π ( r 1 2 r 2 2 ) h = [ 22 7 ( ( 0.35 ) 2 ( 0.05 ) ) 2 × 14 ] c m 3 = [ 22 7 ( 0.1225 0.0025 ) × 14 ] c m 3 = ( 44 × 0.12 ) c m 3 = 5.28 c m 3
Volume of the graphite
= π r 2 2 h = [ 22 7 × ( 0.05 ) 2 × 14 ] c m 3 = ( 44 × 0.0025 ) c m 3 = 0.11 c m 3

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