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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 and that

Q : 7     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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Given,

Length of the cylindrical pencil = h = 14\ cm

The radius of the graphite (Inner solid cylinder)  = r_1 = \frac{1}{2}\ mm = 0.05\ cm

Radius of the pencil (Inner solid graphite cylinder + Hollow wooden cylinder) =

r_2 = \frac{7}{2}\ mm = 0.35\ cm

We know, Volume of a cylinder= \pi r^2 h

\therefore The volume of graphite = \pi r_1^2 h

\\ = \frac{22}{7}\times 0.05^2 \times14 \\ = 44\times0.0025 \\ = 0.11\ cm^3

And, Volume of wood = \pi (r_2^2- r_1^2) h

\\ = \frac{22}{7}\times (0.35^2-0.05^2) \times14 \\ = 44\times(0.35-0.05)(0.35+0.05) \\ = 44\times(0.30)(0.40) \\ = 5.28 \ cm^3

Therefore, the volume of wood is 5.28 \ cm^3 and the volume of graphite is 0.11 \ cm^3

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