Q. 145.0( 6 Votes )

A lead pencil con

Answer :


Concept Used: Volume of the wood = Volume of a pencil – volume graphite


Volume of Cylinder = πr2h


Where r = radius of the cylinder and h = height of the cylinder


Given: Diameter of pencil = 7 mm


Diameter of graphite = 1 mm


Length of the pencil = 14 cm


Assumption: Let r1 be the radius of pencil, r2 be the radius of graphite and h be the height of pencil.


Explanation:


Radius


Radius (pencil), r1 mm = 0.35 cm


Radius (graphite), r2 mm = 0.05 cm


Height (Pencil), h = 14 cm


Volume of wood in pencil = π (r12 – r22) h


= [(0.35)2 – (0.05)2 × 14]


= (0.1225 – 0.0025) × 14


= 44 × 0.12


= 5.28 cm3


Volume of graphite = πr22h


= × (0.05)2 × 14


= 44 × 0.0025


= 0.11 cm3


Hence, The volume of wood in pencil is 5.28 cm3 and volume of graphite in pencil is 0.11 cm3.


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