Question

A lead pencil consist of a cylinder of wood with a solid cylinder of graphite filled in to it . The diameter of the pencil is 7 mm ,the diameter of graphite

Answer 1

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

___________

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

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

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

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

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

___________

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

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

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

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

Answer 2

Here, h = 14 cm.

Radius of the pencil (R) = 7/ 2 mm = 0.35 cm.

Radius of the graphite (r) = 1/ 2 mm = 0.05 cm.

Volume of the the graphite = π r2h

= 22/ 7 × 0.05 × 0.05 × 14 cm³ = 0.11 cm³

Volume of the the wood = π (R2 – r2)h

= 22/ 7 × [(0.35)2 – (0.05)2] × 14 cm3

= 22/ 7 × 0.4 × 0.3 × 14 cm3 = 5.28 cm³

Hence, volume of the wood = 5.28 cm³ and volume of the graphite

= 0.11 cm³