Question

a lead pencil consists of a cylinder of wood is a solid cylinder of graphite filled in the interior the diameter of the pencil is 7 millimetre and the diameter of the graphite is 1 mm if the length of the pencil is 14 cm find the volume of the wood and that of the graphite

Answer 1

Answer:

Graphite's volume => 110 mm³

The wood's volume => 5280 mm³

Step-by-step explanation:

Radius of the pencil = 3.5 mm = R, Height of the pencil = 140 mm = h, Radius of the graphite cylinder = 0.5 mm = r

(a) The volume of the graphite :

The diameter of the graphite = 1 mm

Height= Height of the pencil = 140 mm

Volume of the graphite = πr²h

=> (22/7)×0.5²×140 => (22/7)×35 = 22×5

=> 110 mm³

(b) Volume of the wood = Volume of a hollow cylinder

=> π(R²-r²)h

=> 22/7(3.5²-0.5²)140 => 22/7(12)140 = 22×12×20

=> 5280 mm³

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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

___________

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

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

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

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

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

___________

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

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

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

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