Question

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5. Find the total surface area of a cylindrical tank whose capacity is 5632 m' and height is 28 m​

Answer 1

$\star\;{\underline{\frak{AnswEr\;:}}}$

$\setlength{\unitlength}{1.5 cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(2.3,1){\vector(0,1){1.5}}\put(2.3,1){\vector(0, - 1){1.2}}\put(2.3,1){ \bf 28 \: m }\put(0.3,0.1){ \bf r }\put(0,0){\vector(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5)\put(0.5,1){ \bf 5632 \: m^3 }\end{picture}$

⠀⠀⠀

$\sf GivEn \begin{cases}& \sf{Volume\;of\; cylindrical\;tank = \bf{5632\;m^3}} \\ & \sf{Height\;of\; cylindrical\;tank = \bf{28\;m}} \end{cases}$

We have to find, Total surface area of cylindrical tank.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\star\;{\underline{\frak{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\purple{Volume_{(cylinder)} = \pi r^2h}}}}$

$:\implies\sf \dfrac{22}{ \cancel{7}} \times r^2 \times \cancel{28} = 5632$

$:\implies\sf 22 \times r^2 \times 3 = 5632$

$:\implies\sf 88 \times r^2 = 5632$

$:\implies\sf r^2 = \cancel{ \dfrac{5632}{88}}$

$:\implies\sf r^2 = 64$

$:\implies\sf \sqrt{r^2} = \sqrt{64}$

$:\implies{\boxed{\frak{\pink{r = 8\;m}}}}\bigstar$

$\therefore\;{\underline{\sf{Radius\;of\; cylindrical\; tank\;is\; \bf{8\;m}.}}}\;$

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀☯ Now, Finding Total Surface Area of Cylindrical tank,

$\star\;{\underline{\frak{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\purple{TSA_{(cylinder)} = 2 \pi r(h + r)}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times 8 \bigg( 28 + 8 \bigg)$

$:\implies\sf 2 \times \dfrac{22}{7} \times 8 \bigg( 36 \bigg)$

$:\implies\sf 2 \times \dfrac{22}{7} \times 288$

$:\implies\sf \cancel{\dfrac{12672}{7}}$

$:\implies{\boxed{\frak{\pink{1810.285\;m^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Total\;Surface\;area\;of\; cylindrical\; tank\;is\; \bf{1810.285\;m^2}.}}}$