An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil and the diameter of the graphite is given. Find the volume of the wood and that of the graphite.

This is the Question Number 20, Exercise 17.1 of M.L Aggarwal.

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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 of the graphite.. This is the Question Number 07, Exercise 17.1 of M.L Aggarwal.

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Given length of the pencil, h = 14 cmDiameter of the pencil = 7 mmradius, R = 7/2 mm = 7/20 cmDiameter of the graphite = 1 mmRadius of graphite, r = ½ mm = 1/20cmVolume of graphite = r^{2}h= (22/7)×(1/20)^{2}×14= 11/100= 0.11 cm^{3}Hence the volume of the graphite is 0.11 cm^{3}Volume of the wood = (R^{2}-r^{2})h= (22/7)×[(7/20)^{2}-(1/20)^{2}]14= (22/7)×[(49/400)-(1/400)]14= (22/7)×(48/400)×14= 11×12/25= 5.28 cm^{3}Hence the volume of the wood is 5.28 cm^{3}