Question

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

Answer 1

hii!!

here's ur answer...

given the diameter of the graphite filled in the pencil is 1mm. therefore radius = 0.5mm

height (length) of the pencil is 14cm

in mm = 14×10

= 140mm

volume of the graphite = πr²h

= 22/7×0.5×0.5×140

= 22×0.5×0.5×20

= 110mm³

diameter of the pencil = 7mm, therefore radius = 7/2mm

volume of the pencil = πr²h

= 22/7×7/2×7/2×140

= 11×7×70

= 5390mm³

hence volume of the wood in the pencil = 5390-110

= 5280mm³

hope this helps..!

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

___________

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

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

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

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

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

___________

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

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

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

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