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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.

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2580 mm3

5280 mm3

2850 mm3

5380 mm3

answer is B.

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Detailed Solution

Given,
Radius of the pencil

= 72 mm

.
Height of the pencil

= 14

cm.
We know 1 cm=10 mm.

⇒

h=140 mm.
Volume of the pencil will be,

⇒

π r 2 h

⇒ 227 × 722 × 140

⇒ 5390 m m 3

Radius of the graphite

= 12 m m

Volume of the graphite,

⇒

π r 2 h

⇒ 227 × 122 × 140

⇒ 110 m m 3

Volume of the wood =Volume of the pencil-Volume of the graphite

⇒ (5390 − 110) m m 3

⇒ 5280 m m 3

So, the volume of the wood is 5280 mm3.
Therefore, the correct option is 2.

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