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)
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
Volume of graphite = r22h cubic units
Substitute the values, we have
= (22/7) × 0.052 × 14
= 44 × 0.0025
= 0.11
The volume of graphite is 0.11 cm3.