Question

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of at the pencil is $7mm$ and the diameter of the graphite is $1mm$. If the length of the pencil is $14cm$, find the volume of the wood and that of the graphite.

Answer 1

Given:

$\Rightarrow$Radius of pencil $=\frac{7}{2}mm=3.5$mm

$\Rightarrow$$0.35$cm $=r_p$

$\Rightarrow$$h=14$cm,

Radius of graphite $=\frac{1}{2}$mm$=0.05$cm

$\Rightarrow$Volume of wood in pencil $=\pi (r_p^2-r_g^2)h$

$\Rightarrow$$\frac{22}{7}[{\left(0.35\right)}^2-{\left(0.05\right)}^2]14$

$\Rightarrow$$\frac{22}{7}(0.1225-0.0025)\times 14$

$\Rightarrow$$44\times 0.12=5.28$cm${}^3$

$\Rightarrow$Volume of a graphite $=\pi r_g^{2}h$

$\Rightarrow$$\frac{22}{7}\times {\left(0.05\right)}^2\times 14$cm${}^3$

$\Rightarrow$$44\times 0.0025$cm${}^3$

$\Rightarrow$$0.11$cm${}^3$