Question

A lead of pencil contist of celendar if wood with a cylinder of a graphite filled in interior . The diameter of the pencil is 7 mm and the diameter of 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

volume of wood = π × 7^2 × 140 = 6860π mm^3
volume of graphite = π × 1^2 × 140 = 140π mm^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

___________

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

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

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

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

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

___________

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

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

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

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