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

diameter of pencil - 7mm/0.7cm, radius-0.35
diameter of graphite - 1mm/0.1cm, radius-0.05

Volume of wood = πh( R^2 - r^2)
= 22/7 × 14 (0.35^2 - 0.05^2)
= 44(0.1225 - 0.0025)
= 44 × 0.12
= 5.28cm^3

Volume of graphite = 22/7 × 0.0025 × 14
= 0.11cm^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

___________

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

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

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

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

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

___________

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

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

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

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