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
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Answer:
Volume of graphite
[tex] \sf Radius \: of \: Graphite = r = \dfrac{Diameter \: of \: graphite}{2}= \dfrac{1}{2} mm [/tex]
[tex] \displaystyle \: \frac{1}{2} \times \frac{1}{10} = \frac{1}{20} cm[/tex]
Height of graphite = h = 14 cm
[tex] \sf \: volume \: of \: graphite \: cylinder \: = \pi {r}^{2} h[/tex]
[tex] \displaystyle \sf\: ( \frac{22}{7} \times \frac{1}{20} \times \frac{1}{20} \times 14)m {m}^{3} [/tex]
[tex] \displaystyle \sf \: (22 \times \frac{1}{1} \times \frac{1}{20} \times 2)[/tex]
[tex] \displaystyle \sf \: = 0.11c {m}^{3} [/tex]
Volume of pencil
[tex] Radius \: of \: pencil = \dfrac{ Diameter \: of \: pencil}{2} = \dfrac{1}{2} [/tex]
[tex] \displaystyle= \frac{7}{20} cm[/tex]
[tex] \displaystyle \: \frac{22}{7} \times \frac{7}{20} \times \frac{7}{20} \times 14)[/tex]
[tex] \displaystyle \: 5.39c {m}^{ 3} [/tex]
Volume of wood = Volume of pencil - Volume of graphite.
[tex] \sf \therefore \: volume \: of \: wood \: = 5.39 - 0.11 = 5.28c {m}^{3} [/tex]
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