Question

Three thin walled long circular cylinders 1. 2. 3 of diameters 15 cm (e - 005), 29 cm
(-0.1), and 35 cm (0.2) respectively are arranged concentrcally Temperature of
cylinder 1 is 80 K and that of cylinder 3 is 300 K. Assuming that there is vacuum de
annular spaces, determine the steady state temperature attamed by cylinder 2​

Answer 1

$\huge{\underline{\sf{\green{Solution-}}}}$

$\underline\green{\sf Given -}$

$\longrightarrow \sf{h = 1m}$

$\longrightarrow \sf{Volume = 15.4 l}$

$\underline\green{\sf Find -}$

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Volume of Cylinder = $\huge{\underline{\sf{\green{\pi{r}^{2}h}}}}$

$\longrightarrow \sf{\pi{r}^{2}h \: = \: 1.54\times1000}$

$\longrightarrow \sf{= \dfrac{22}{7}\times{r}^{2}\times(100) = 1.54\times1000}$

$\longrightarrow \sf{{r}^{2} = \dfrac{1.54 \: \times \: 1000 \: \times 7} {22 \: \times 100}}$

$\longrightarrow \sf{{r}^{2}= 49}$

$\longrightarrow \sf{r = \sqrt{49}}$

$\longrightarrow \sf\green{r = 7cm}$

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TSA of cylinder =$\huge{\underline{\sf{\green{2 \pi r(r+h)}}}}$

$\longrightarrow \sf{=2\times\dfrac{22}{7}(7+100)}$

$\longrightarrow \sf{=44\times107}$

$\longrightarrow \sf\green{= 4708{cm}^{2}}$

${: 4708{cm}^{2} = ?{m}{2}:4708cm}$

$\longrightarrow \sf{\dfrac{4708}{100\times100}{m}^{2}}$

$\longrightarrow \sf\green{ = 0.4708{m}^{2}}$

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