Question

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 dimeter 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.

Answer 1

Here, h = 14 cm. 

Radius of the pencil (R) = 7/ 2 mm = 0.35 cm. 

Radius of the graphite (r) = 1/ 2 mm = 0.05 cm. 

Volume of the the graphite = π r²h 

= 22/ 7 × 0.05 × 0.05 × 14 cm³ = 0.11 cm³ 

Volume of the the wood = π (R² – r²)h 

= 22/ 7 × [(0.35)² – (0.05)²] × 14 cm³ 

= 22/ 7 × 0.4 × 0.3 × 14 cm³ = 5.28 cm³ 

Hence, volume of the wood = 5.28 cm³ and volume of the graphite 

= 0.11 cm³ Ans