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 1 mm.If the length of the pencil is 14 cm, find the volume of the wood and that of the graphite.
$[Assume\pi =\frac{22}{7}]$

Answer 1

Radius $\left(r_1\right)$ of the pencil $=\left(\frac{7}{2}\right)mm=(\frac{0.7}{2}cm=0.35cm)(10mm=1cm)$

Radius $\left(r_2\right)$ of the graphite $=\left(\frac{1}{2}\right)mm=\left(\frac{0.1}{2}\right)cm=0.05cm$

Height (h) of the pencil = 14 cm

Volume of wood in the pencil
$=\pi (r_1^2-r_2^2)h$
$=\left[\frac{22}{7}\left\{\right(0.35{)}^2-(0.05{)}^2\times 14\}\right]c{m}^3$
$=\left[\frac{22}{7}\right(0.1225-0.0025)\times 14]c{m}^3$
$=(44\times 0.12)c{m}^3$
$=5.28c{m}^3$

Volume of the graphite
$=\pi r_2^{2}h=[\frac{22}{7}\times (0.05{)}^2\times 14]c{m}^3$
$=(44\times 0.0025)c{m}^3$
$=0.11c{m}^3$