A lead pencil consists of a cylinder of wood with 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. (Assume π = 22/7)

 Solution:

Radius of pencil, r1 = 7/2 mm = 0.7/2 cm = 0.35 cm

Radius of graphite, r2 = 1/2 mm = 0.1/2 cm = 0.05 cm

Height of pencil, h = 14 cm

Formula to find, volume of wood in pencil = (r12-r22)h cubic units

Substitute the values, we have

= [(22/7)×(0.352-0.052)×14]

= 44×0.12

= 5.28

This implies, volume of wood in pencil = 5.28 cm3

Again,

Volume of graphite = r22h cubic units

Substitute the values, we have

= (22/7)×0.052×14

= 44×0.0025

= 0.11

So, the volume of graphite is 0.11 cm3.