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Question

A lead pencil consist of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7mm and the graphite is 1mm. If the length of the pencil is 14cm, find the volume of the wood and that of the graphite


Solution

Diameter of pencil$$=7 mm$$

$$r{\rm (graphite)}=\dfrac{1}{2}mm=0.2 cm$$

$$\hbox{Volume of cylinder}=\pi r^2h$$

$$=\left(\dfrac{22}{7}\times\dfrac{1}{20}\times \dfrac{1}{20}\times 14 \right )cm^3$$

$$=\left(11\times\dfrac{1}{10}\times \dfrac{1}{10} \right )cm^3$$

$$=0.11 cm^3$$

volume of wood $$=$$volume of pencil-volume of graphite

$$=\pi r^2h-0.11 cm^3$$

$$=\dfrac{22}{\not 7}\times\left(\dfrac{\not 7}{2}\times \dfrac{1}{10} \right )\left(\dfrac{7}{2}\times\dfrac{1}{10} \right )\times 14-0.11$$

$$=\dfrac{11}{20}\times \dfrac{49}{10}-0.11$$

$$=5.39-0.11$$

$$=5.20 cm^3$$


Mathematics

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