 Fiona Chung

2023-03-27

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 $\pi =\frac{22}{7}$] nelagodafsed

Radius (${r}_{1}$) of the pencil $=\left(\frac{7}{2}\right)mm=\left(\frac{0.7}{2}cm=0.35cm\right)\left(10mm=1cm\right)$
Radius (${r}_{2}$) 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
$=\pi \left({r}_{1}^{2}-{r}_{2}^{2}\right)h\phantom{\rule{0ex}{0ex}}=\left[\frac{22}{7}\left(\left(0.35{\right)}^{2}-\left(0.05\right){\right)}^{2}×14\right]c{m}^{3}\phantom{\rule{0ex}{0ex}}=\left[\frac{22}{7}\left(0.1225-0.0025\right)×14\right]c{m}^{3}\phantom{\rule{0ex}{0ex}}=\left(44×0.12\right)c{m}^{3}\phantom{\rule{0ex}{0ex}}=5.28c{m}^{3}$
Volume of the graphite
$=\pi {r}_{2}^{2}h=\left[\frac{22}{7}×\left(0.05{\right)}^{2}×14\right]c{m}^{3}\phantom{\rule{0ex}{0ex}}=\left(44×0.0025\right)c{m}^{3}\phantom{\rule{0ex}{0ex}}=0.11c{m}^{3}$

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