Question

a lead
pencil consists of a cylinder of wood with a solid cylinder of graphite filled in
interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm
The length of the pencil is 14 cm. find the volume of the wood and that of the
A lead pencil consists of a
graphite
Seni​

Answer 1

for a cylindrical lead pencil,

d : 7mm

then, r : 3.5mm

length of the pencil (h) : 14cm=140mm

for a graphite,

d=1mm

then , r = 0.5mm

here, volume of lead

=total area of graphite

volume of cylinder =πr²h

=3.14×3.5×3.5×140

=31.4×3.5×3.5×14

=109.90×49

=5386.1 cu.cm

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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

___________

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

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

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

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

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

___________

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

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

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

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