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A lead pencil consists of a …

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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 7mm and the diameter of the graphite is 1mm. If the length of the pencil is 14cm, find the volume of the wood and that of the graphite.

    • Posted by Joseph M Jose 5 years, 4 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 4 months ago

    Solution:

    Given:
    Diameter of the pencil =7mm

    Radius of the pencil (R) = 7/2mm

    Diameter of the graphite cylinder =1mm

    Radius of the graphite(r) = 1/2mm

    Height(h)=14cm= 140mm

    [1cm= 10 mm]

    Volume of a cylinder= πr²h

    Volume of graphite cylinder = πr2h = 22/7 ×1/2 × 1/2 ×140

    Volume of graphite = 110 mm³

     

    Volume of pencil = πR²h

     = 22/7 ×7/2 × 7/2 ×140

    = 490×11= 5390 mm²

    Volume of pencil=5390mm³

     

     Volume of wood = Volume of pencil - Volume of graphite

     Volume of wood= 5390- 110= 5280 mm³

    = 5280/1000= 5.28 cm³

    [1mm³= 1/1000cm³]

    Volume of wood = 5.28 cm³

    Or

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