Question

a lead pencil consist 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

Answer 1

$\bold{\huge{\underline{\underline{\rm{ Question :}}}}} \:$

A lead pencil consist 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 ,Volume of wood, weight of whole pencil,if the specific gravity of wood is 0.73/cm^3 and that of graphite is 2.1g cm^3

___________________________

$\small{\huge{\underline{\underline{\rm{ Given :}}}}} \:$

The diameter of the pencil = 7mm

The diameter of a graphite = 1mm

Length of a pencil = 14 cm

$\bold{\huge{\underline{\underline{\rm{ To \: Find:}}}}}$

1. Volume of graphite, Volume of wood

2. Weight of whole pencil

$\bold{\huge{\underline{\underline{\rm{ Solution :}}}}} \:$

Diameter of graphite cylinder = 1mm = 1/10 cm

Radius of graphite cylinder = (1/2 × 1/10)cm =1/ 20cm

Length of graphite cylinder = 14 cm

$\text{Volume of graphite cylinder} = \pi { \text{r}}^{2} \text{h} { \text{cm}}^{3}$

$=( \frac{ \cancel{22}}{ \cancel7} \times \frac{1}{ \cancel{20}} \times \frac{1}{ \cancel{20}} \times \cancel 14) { \text{cm}}^{3}$

$= \frac{11}{100} { \text{cm}}^{3} = 0.11 { \text{cm}}^{3}$

$\bold{\huge{\underline{\underline{\rm{ Now \: }}}}}$

$\text{Diameter of pencil} = 7 \text{mm}= \frac{7}{10} \: \text{cm} \:$

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

$\text{Length of pencil = 14 cm}$

$\text{Volume of pencil } = \pi { \text{r}}^{2} \text{h {cm}}^{3}$

$=( \frac{22}{7} \times \frac{7}{20} \times \frac{7}{20} \times 14) { \text{cm}}^{3}$

$= \frac{539}{100} { \text{cm}}^{3} = 5.39 { \text{cm}}^{3}$

___________________________

____

Therefore

Volume of wood in pencil

= ( Volume of pencil ) - ( volume of graphite )

= ( 5.39 - 0.11 ) cm^3

= 5.28 cm ^3

Answer 2

Given :

• Radius of pencil $\tt{ = \frac{7}{2} \: mm = \frac{0.7}{2} \: cm arrow0.35 \: cm}$

• Radius of graphite $\tt{ = \frac{1}{2} \: mm = \frac{0.1}{2} \: cm arrow0.05 \: cm}$

• Height of pencil = 14 cm

___________

$\sf \gray{Volume \: of \: wood \: in \: pencil = \pi( {r}^{2} _{1} - {r}^{2} _{2} )h}$

$\sf{ = \frac{22}{7} \times ( {0.35)}^{2} - ( {0.05)}^{2} \times 14 \: cm {}^{3} }$

$\sf{ = \frac{22}{7} \times 0.1225 \times 0.0025 \times 14 \: cm {}^{3} }$

$\sf{ =44 \times 0.12 } \: cm {}^{3}$

$\sf \boxed {\sf \red{ = 5.28 \: cm {}^{3} }}$

___________

$\therefore \sf \gray{Volume \: of \: graphite = \pi {r}^{2} h}$

$\sf{ = \frac{22}{7} \times {(0.05)}^{2} \times 14 \: cm {}^{3} }$

$\sf{ = 44 \times 0.0025 \: cm {}^{3} }$

$\boxed{\sf \red{ = 0.11\: cm {}^{3}}}$