Question

A metal pipe has a bore (internal diameter) of 5 cm. The pipe is 2 mm thick all around. find the mass of 2 m long pipe if 1 cm^3 of the metal has a mass of 7.7 g.

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Answer 1

Answer:

Valency :-

• It is the combining capacity of an element. It is the number of electrons lost, gained or shared during a chemical reaction.

Answer 2

QuestioN

• A metal pipe has a bore (internal diameter) of 5 cm. The pipe is 2 mm thick all around. find the mass of 2 m long pipe if 1 cm^3 of the metal has a mass of 7.7 g.

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${\bold { \underline{\small{Let }}}}$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet\: r \:be\:the\:internal\:radius$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\bullet\: R\:be\:the\: external\:radius$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\succ h\:be\:its\:height$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:━━━━━━━━━━━━━━━━━━$

${\bold { \underline{\small{Then, }}}}$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: r\:=\:\bf\dfrac{5}{2}cm$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\normalsize\mathtt\purple{R\:=\:r+thickness}$

$\:$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\bigg(\bf\dfrac{5}{2}+\bf\dfrac{2}{10}\bigg)cm$

$\:$

$\sf \:\:\:\:\:\:\:\:\:\:=\: \bigg(\bf\dfrac{25+2}{10}\bigg)cm\:\:\:=\:\:\:\bf\dfrac{27}{10}cm$

$\:$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{\large{\frak{\pmb{\underline{\orange{ h=\:2\:m = 200\:cm}}}}}}$

$\:\:\:\:\:\:\:\:\:\:\:───────────────────$

$\:$

${\bold { \underline{\small{Now, }}}}$

${\succ \small {\underline{\boxed{\mathcal{\underline{\pink{ Volume_{(metal)} = External \: vol. - Internal \:vol.}}}}}}}$

$\:$

$\tt \:\:\leadsto\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \:\pi R^2h -\pi r^2h$

$\:$

$\tt \:\:\leadsto\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \pi (R^2-r^2)h$

$\:$

$\sf \: \twoheadrightarrow\:\Bigg\{ \bf\dfrac{22}{7}\bigg[ \Big(\bf\dfrac{27}{10}\Big)^2-\Big( \bf\dfrac{5}{2}\Big)^2\bigg]\times 200\Bigg\}\:cm^3$

$\:\:$

$\sf \: \twoheadrightarrow\: \Bigg\{ \bf\dfrac{22}{7}\bigg[ \Big(\bf\dfrac{729}{100}\Big)-\Big( \bf\dfrac{25}{4}\Big)\bigg]\times 200\Bigg\}\:cm^3$

$\:\:$

$\sf \:\:\:\: \twoheadrightarrow\:\bigg\{ \bf\dfrac{22}{7}\Big[\bf\dfrac{729-625}{100}\Big]\times 200\bigg\}\:cm^3$

$\:\:$

$\sf \:\:\:\:\:\:\:\:\:\:\: \twoheadrightarrow\:\bigg( \bf\dfrac{22}{7}\times \bf\dfrac{104}{100}\times 200\bigg)\:cm^3$

$\:$

$\:\:\small{\underline{\mathcal{\green{Mass\:of\:1\:cm^3\:of\:the\:metal\:=\:7.7\:g }}}}$

$\:\:$

$\sf \therefore\:Mass\:of\:\bf\dfrac{4576}{7}\:cm^3\:of\:the\:metal=\bf\dfrac{7.7\times 4576}{7}\:g$

$\:$

$\sf \:\:\:\:\:\:\:\:\:\:\:\:=\bf\dfrac{7.7\times 4576}{7\times 1000}\:kg$

$\:$

$\:\:\:\:\:\:\ddagger\underline{\boxed{\sf{Mass\:of\:the\:metal\: pipe\:=\frak{\red{5.0336\:kg}}}}}$