Question

The radi of two cylinders are in the ratio 5:7 and their heights are in the ratio 3:5. The ratio of their curved surface area is ​

Answer 1

Step-by-step explanation:

$\underline{\bf{\dag} \:\mathfrak{Given\; that\: :}}$⠀⠀

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The radius of two cylinders are in the ratio of 5:7.

$:\implies\sf r_{1} : r_{2} = 5 : 7$

Also,

And, their heights are in the ratio of 3:5.

$:\implies\sf h_{1} : h_{2} = 3:5$

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀

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$\star\;\boxed{\sf{\pink{CSA_{\;(cylinder)} = 2\pi r h}}}$

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$:\implies\sf CSA_{\:(ratio)} = \bigg(\dfrac{2\pi r_{1} h_{1}}{2\pi r_2 h_2}\bigg) \\\\\\:\implies\sf CSA_{\:(ratio)} = \Bigg(\dfrac{\cancel{\;2}\; \times \cancel{\frac{22}{7}} \times 5 \times 3}{\cancel{\;2}\times \cancel{\frac{22}{7}} \times 7 \times 5} \Bigg) \\\\\\:\implies\sf CSA_{\:(ratio)} = \cancel\dfrac{15}{35}\\\\\\:\implies\sf CSA_{\:(ratio)} = \dfrac{3}{7}\\\\\\:\implies{\underline{\boxed{\sf{\pink{CSA_{\;(ratio)} = 3:7}}}}}\;\bigstar$

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$\therefore{\underline{\sf{Hence, \; the\; ratio \; of \: their \: CSA \; is \; \bf{3:7 }.}}}$

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$\qquad\boxed{\underline{\underline{\purple{\bigstar \: \bf\:Formula\:Related\:to\:cylinder\:\bigstar}}}}$

$\sf Area\:of\:base\:of\:cylinder = \bf{\pi r^2}$

$\sf Total\:Surface\:area\:of\:cylinder = \bf{2 \pi r(r + h)}$

$\sf Curved\:Surface\:area\:of\:cylinder = \bf{2 \pi rh}$

$\sf Volume\:of\:cone = \bf{ \dfrac{1}{3} \times Volume_{\:(cylinder)}}$

Answer 2

Answer:

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The radi of two cylinders are in the ratio 5:7 and their heights are in the ratio 3:5. The ratio of their curved surface area is ​

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Step-by-step explanation: