Question

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm 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

Given:

Radius of pencil = 7

2

Therefore radius = 3.5 mm

p

h=14cm,

Radius of graphite = 1

2

= 0.05cm

⇒Volume of wood in pencil =π(r of pencil2 −r of graphite2 ) × h (2 means square)

⇒ 22

7 into [(0.35)2 −(0.05)2 ]14

⇒ 22

7 into (0.1225−0.0025)×14

⇒44×0.12 = 5.28cm3 (3 means cube)

⇒Volume of a graphite =πr of graphite2 × h (2 means square)

⇒ 22

7 × (0.05)2 × 14cm3) (3 means cube)

⇒ 44×0.0025cm3 (3 means cube)

⇒0.11cm3 (3 means cube)

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

___________

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

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

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

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

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

___________

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

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

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

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