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ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.1 in Chapter 17 - Mensuration
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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.
Solution:
The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula π r2h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder.
Given length of the pencil, h = 14 cm
Diameter of the pencil = 7 mm
radius, R = 7/2 mm = 7/20 cm
Diameter of the graphite = 1 mm
Radius of graphite, r = ½ mm = 1/20cm
Volume of graphite = π r2h
= (22/7)×(1/20)2×14
= 11/100
= 0.11 cm3
Hence the volume of the graphite is 0.11 cm3
Volume of the wood = π (R2-r2)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 cm3
Hence the volume of the wood is 5.28 cm3 
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