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 $7mm$ 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

$\Rightarrow$ Radius of graphite $=r=\frac{1}{2}mm=\frac{1}{2}\times \frac{1}{10}=\frac{1}{20}cm$

$\Rightarrow$ Height of graphite $=h=14cm$

$\Rightarrow$ Volume of the graphite cylinder $=\pi r^{2}h$

$=(\frac{22}{7}\times \frac{1}{20}\times \frac{1}{20}\times 14)c{m}^3$

$=0.11c{m}^3$

$\Rightarrow$ Radius of pencil $=r=\frac{7}{2}mm=\frac{7}{2}\times \frac{1}{10}cm=\frac{7}{20}cm$

$\Rightarrow$ Height of the pencil $=h=14cm$

$\Rightarrow$ Volume of the pencil $=\pi r^{2}h$

$=(\frac{22}{7}\times \frac{7}{20}\times \frac{7}{20}\times 14)c{m}^3$

$=5.39c{m}^3$

$\Rightarrow$ Volume of wood = Volume of pencil - Volume of graphite

$\Rightarrow$ Volume of wood $=(5.39-0.11)c{m}^3=5.28c{m}^3$