Question

A lead pencil consists of a cylinder of wood with 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. (Assume$\pi =\frac{22}{7}$)

Answer 1

Step 1: Write the given dimensions

Height of wood (and graphite) cylinder$h=14cm=140mm$

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

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

Step 2: Find the volume of the graphite

Volume of Graphite $=\left(\pi r^{2}h\right)$

$$\begin{gathered} =\frac{22}{7}\times \frac{1}{2}\times \frac{1}{2}\times 140m{m}^3 \\ =110m{m}^3 \\ =0.11c{m}^3 \end{gathered}$$

Step 3: Find the volume of the graphite

Volume of wood $=$ Volume of pencil – Volume of graphite

$$\begin{gathered} =\left(\pi R^{2}h\right)–\left(\pi r^{2}h\right) \\ =\pi (R^2–r^2)h \\ =\frac{22}{7}\left[{\left(\frac{7}{2}\right)}^2-{\left(\frac{1}{2}\right)}^2\right]x140 \\ =22\times 20\times (49/4-1/4) \\ =22\times 20\times 12 \\ =5280mm3 \\ =52.80cm3 \end{gathered}$$

Hence, the volume of the wood and that of the graphite are $52.80c{m}^3$ and $0.11c{m}^3$ respectively.