Question

the radii of two right circular cylinder are in the ratio 2:3 and their height are in the ratio 5:4 .Calculate the ratio of their curved surface areas.

Answer 1

5 is to 9 is the volume

Answer 2

$\large\underline\mathfrak{Given:-}$

• $\: \: \: \: \: {Ratio \: \: of \: \: radii \: \: of \: \: two \: \: circular \: \: cylinder \: \: = \: \: 2 \: : \: 3}$

• $\: \: \: \: \: {Ratio \: \: of \: \: height \: \: of \: \: two \: \: circular \: \: cylinder \: \: = \: \: 5 \: : \: 4}$

$\large\underline\mathfrak{To \: \: Find:-}$

• $\: \: \: \: \: Ratio \: \: of \: \: their \: \: curved\: \: surface \: \: area \: ?$

$\huge\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: let \: \: the \: \: radii \: \: of \: \: two \: \: circular \: \: cylinder \: \: be \: \: 2 \: x \: \: and \: \: 3 \: x.$

• $\: \: \: \: \: let \: \: the \: \: height \: \: of \: \: two \: \: circular \: \: cylinder \: \: be \: \: 5 \: y \: \: and \: \: 4 \: y.$

$\large\underline\mathbb{Curved \: \: surface \: \: area \: \: of \: \: cylinder:-}$

$\: \: \: \: \: \large\fbox{CSA \: \: = \: \: 2 \: π \: r \: h}$

• $\underline\mathbb{CSA \: \: of \: 1 \: st \: \: cylinder \: \: having \: \: radius \: \: 2 \: x \: \: and \: \: height \: \: 5 \: y}$

$\: \: \: \: \: \leadsto {CSA \: \: = \: \: 2 \: π \: 2 \: x \: 5 \: y}$

$\: \: \: \: \: \leadsto {CSA \: \: = \: \: 20 \: π \: xy}$

• $\underline\mathbb{CSA \: \: of \: 2 \: nd \: \: cylinder \: \: having \: \: radius \: \: 3 \: x \: \: and \: \: height \: \: 4 \: y}$

$\: \: \: \: \: \leadsto {CSA \: \: = \: \: 2 \: π \: 3 \: x \: 4 \: y}$

$\: \: \: \: \: \leadsto {CSA \: \: = \: \: 24 \: π \: xy}$

$\underline\mathfrak{Now, \: \: radius \: \: of \: \: curved \: \: surface \: \: area \: \: of \: \: both \: \: cylinder \: \: is:-}$

$\: \: \: \: \: \leadsto \: \frac{CSA \: \: of \: \: 1 \: st \: cylinder}{CSA \: \: of \: \: 2 \: nd \: cylinder}$

$\: \: \: \: \: \leadsto \: \frac{20 \: π \: xy}{24 \: π \: xy}$

$\: \: \: \: \: \leadsto \: \frac{20}{24}$

$\: \: \: \: \: \leadsto \: \frac{5}{6}$

$\fbox{So, \: \: ratio \: \: of \: \: curved \: \: surface \: \: area \: \: of \: \: both \: \: both \: \: cylinder's \: \: is \: \: 5 \: : \: 6}$

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