Question

A pencil of diameter 10.5mm and length 14.4 cm has a lead of diameter 1.75 mm. Find the volume of the wood and of the lead used in making 100 pencils.

Answer 1

Dear student
$$\begin{gathered} \mathrm{dia}10.5\mathrm{mm}\mathrm{length}14.4\mathrm{lead}\mathrm{dia}1.75\mathrm{mm} \\ \mathrm{Diameter}\mathrm{of}\mathrm{pencil}=10.5\mathrm{mm}=\frac{10.5}{10}\mathrm{cm} \\ \mathrm{Radius}\mathrm{of}\mathrm{pencil},{\mathrm{r}}_1=\frac{10.5}{20}\mathrm{cm}=0.525\mathrm{cm} \\ \mathrm{Radius}\mathrm{of}\mathrm{lead},{\mathrm{r}}_2=\frac{1.75}{20}\mathrm{cm}=0.0875\mathrm{cm} \\ \mathrm{Height}\mathrm{of}\mathrm{pencil},\mathrm{h}=14.4\mathrm{cm} \\ \mathrm{Volume}\mathrm{of}\mathrm{wood}\mathrm{in}\mathrm{pencil}=\mathrm{\pi }\left({{\mathrm{r}}_1}^2-{{\mathrm{r}}_2}^2\right)\mathrm{h} \\ =\frac{22}{7}\left[{\left(0.525\right)}^2-{\left(0.0875\right)}^2\right]14.4 \\ =\frac{22}{7}\left(0.275625-0.00765625\right)14.4 \\ =\frac{22}{7}\times 0.27\times 14.4 \\ =12.21{\mathrm{cm}}^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{wood}\mathrm{in}100\mathrm{pencils}=100\times 12.21{\mathrm{cm}}^3=1221{\mathrm{cm}}^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{lead}={{\mathrm{\pi r}}_2}^2\mathrm{h} \\ =\frac{22}{7}\times 0.{0875}^2\times 14.4 \\ =0.3465{\mathrm{cm}}^3 \\ \mathrm{Volume}\mathrm{of}\mathrm{lead}\mathrm{in}100\mathrm{pencils}=100\times 0.3465=34.65{\mathrm{cm}}^3 \end{gathered}$$
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