A lead pencil consists of a cylinder of wood with 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]`

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#### Solution

Radius (*r*_{1}) of pencil = (7/2)mm = (0.7/2)cm = 0.35 cm

Radius (*r*_{2}) of graphite = (1/2)mm = (0.1/2)cm = 0.05 cm

Height (*h*) of pencil = 14 cm

`"Volume of wood in pencil "=pi(r_1^2-r_2^2)h`

`=[22/7{(0.35)^2-(0.05)^2xx14}]cm^3`

`=[22/7(0.1225-0.0025)xx14]cm^3`

= (44 x 0.12) cm3

= 5.28 cm3

`"Volume of graphite "=pir_2^2h=[22/7xx(0.05)^2xx14]cm^3`

= (44 x 0.0025) cm^{3}

= 0.11 cm^{3}

Concept: Volume of a Cylinder

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