 # ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.1 in Chapter 17 - Mensuration

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 Related Questions

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