Question

23. The external radius of a 14 em tong metalnie pipe teem, and the pipela lom thick Find
the volume or the metal used in the piper the mass of 1 cm. metalte 85. And the mass
of the cylinder​

Answer 1

$\underline{\underline{\red{\mathfrak{\huge{ \: Correct \: Question: \: }}}}}$

The external radius of a 14-cm-long metallic pipe is 9cm, and the pipe is 1cm thick. Find the volume of the metal used in the pipe. If the mass of 1cm³ metal is 8.5g. Find the mass of the pipe.

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$\purple{\mathfrak{\huge{Given}}} \begin{cases} \heartsuit\sf External \: Radius \: of \: pipe = 9cm \\ \\ \heartsuit\sf Length \: of \: the \: pipe = 14cm \\ \\ \sf \heartsuit Mass \: of \: 1 {cm}^{3} = 8.5g \\ \\ \sf \heartsuit Thickness \: of \: pipe = 1cm \end{cases}$

$\purple{\mathfrak{\huge{Find}}} \begin{cases} \clubsuit\sf Volume \: of \: metal \: used \: in \: pipe \\ \\ \\ \\ \clubsuit\sf Mass \: of \: the \: pipe\end{cases}$

$\purple{\mathfrak{\huge{Solution}}}$

Here,

☛ External Radius, R = 9cm

☛ Internal Radius, r = 9 - 1 = 8cm

we, know that

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

$\implies\sf Volume \: of \: Pipe = \pi( {R}^{2} - {r}^{2})h$

where,

• π = 3.13
• R = 9cm
• r = 8cm
• h = 14cm

So,

$\dashrightarrow\sf Volume \: of \: Pipe = \pi( {R}^{2} - {r}^{2})h \\ \\ \\ \dashrightarrow\sf Volume \: of \: Pipe = 3.14( {9}^{2} - {8}^{2}) \times 14 \\ \\ \\ \dashrightarrow\sf Volume \: of \: Pipe = 3.14(81 - 64) \times 14 \\ \\ \\ \dashrightarrow\sf Volume \: of \: Pipe = 3.14 \times 17 \times 14 \\ \\ \\ \dashrightarrow\sf Volume \: of \: Pipe = 747.32 {cm}^{3}$

$\therefore\sf The \: Volume \: of \: metal \: used \: is= 747.32 {cm}^{3}$

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Now,

➡ Mass of 1cm³ = 8.5g

➡ Mass of 747.32cm³ = 747.32 × 8.5 = 6352.22g

Hence, Mass of the Pipe = 6352.22g