Question

A lead pencil consists of a wood cylinder with a solid cylinder of graphite fitted into it. The diameter of the pencil is 7 mm. The diameter of the graphite is 1 mm and the length of the pencil is 10 cm. Calculate the weight of the whole pencil in grams if the density of the wood is 0.6 gm/cm^3 and graphite 2.3 gm/cm^3.
Please solve step by step.

Answer 1

ANSWER:

Diameter of the pencil =7mm

Radius of the pencil (R) = 7/2mm

Diameter of the graphite cylinder =1mm

Radius of the graphite(r) = 1/2mm

Height(h)=14cm= 140mm

[1cm= 10 mm]

Volume of a cylinder= πr²h

Volume of graphite

cylinder = πr2h = 22/7 ×1/2 × 1/2 ×140

Volume of graphite

= 110 mm³

Volume of pencil

= πR²h

 = 22/7 ×7/2 × 7/2 ×140

= 490×11= 5390 mm²

Volume of pencil=5390mm³

 Volume of wood = Volume of pencil - Volume of graphite

 Volume of wood= 5390- 110= 5280 mm³

= 5280/1000= 5.28

cm³

[1mm³= 1/1000cm³]

Volume of wood

= 5.28 cm³