Question

A lead pencil consists of a cyalinder of wood with a solid cylindervof graphite filled in the interior .the diameter of thepencil is 7mm and the diameter of the graphite is 1mm .if the length of the pencil is 14cm, find the volume if the wood and that of the graphite.​

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

${\boxed{\sf\:{D\;of\;Pencil}}}$

= 7mm

${\boxed{\sf\:{(R)\;of\;Pencil}}}$

$\tt{\rightarrow\dfrac{7}{2}}$

${\boxed{\sf\:{D\;of\; Graphite\; Cylinder}}}$

= 1mm

${\boxed{\sf\:{Radius}}}$

$\tt{\rightarrow\dfrac{1}{2}}$

${\boxed{\sf\:{Height}}}$

= 14cm

${\boxed{\sf\:{Convert\;it\;into\;mm}}}$

= 140mm

Using Formula we have

${\boxed{\sf\:{Volume\;of\;Cylinder=\pi r^2h}}}$

For Graphite :-

$\tt{\rightarrow\dfrac{22}{7}\times\dfrac{1}{2}\times\dfrac{1}{2}\times 140}$

= 110 mm³

${\boxed{\sf\:{Volume\;of\;Pencil=\pi R^2h}}}$

$\tt{\rightarrow\dfrac{22}{7}\times\dfrac{7}{2}\times\dfrac{7}{2}\times 140}$

= 490 × 11

= 5390 mm²

= 5390mm³

$\textbf{\underline{Volume\;of\; wood}}$

$\large{\boxed{\sf\:{Volume\;of\;pencil-Volume\;of \;graphite}}}$

= 5390 - 110

= 5280 mm³

${\boxed{\sf\:{Convert\;it\;into\;cm^3}}}$

$\tt{\rightarrow\dfrac{5280}{1000}}$

= 5.28 cm³

$\Large{\boxed{\sf\:{Volume\;of\;Wood=5.28\;cm^3}}}$