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 diameter of the graphite is 1mm. If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.

Answer 1

Clearly, for wooden part, which is the form of a hollow cylinder :
External radius (R) = $\frac{7}{2}mm$ = 3.5 mm = 0.35 cm
Internal radius (r) = $\frac{1}{2}mm$ = 0.5 mm = 0.05 cm
And, height (length) = 14 cm.



∴Volume of the wood = π(R² – r²)h = $\frac{22}{7}$ ×[(0.35)² – (0.05)²] ×14 cm³
$\frac{22}{7}$ ×0.12×14 cm³ = 5.28 cm³
And, volume of graphite = π r²h = $\frac{22}{7}$ × (0.05)² × 14 cm³ = 0.11 cm³ .