Question

22. The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio
5:3. Then, the ratio of their volumes is _____
A. 27 : 20 B. 20:27 C. 9:4 D. 4:9
​

Answer 1

Answer:

B 20:27

Step-by-step explanation:

r1/r2=2/3. h1/h2=5/3.

πr²h/πr²h

20:27

hope it helps

Answer 2

Given : The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3.

Exigency to find : The Ratio of their Volumes .

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❍ Let's Consider $\bf r_{1}$ & $\bf r_{2}$ and $\bf h_{1}$ & $\bf h_{2}$ be the radii and Height of two Cylinder's.

Given That ,

• The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3.

Therefore,

$\qquad \longmapsto \sf \dfrac{r_1 }{r_2} = \dfrac{2}{3} \:\:\:and\:\:\:\dfrac{h_1 }{h_2} = \dfrac{5}{3} \:$

$\dag\:\:\it{ As,\:We\:know\:that\::}$

$\qquad \dag\:\:\bigg\lgroup \sf{Volume _{(Cylinder)} \:: \pi r^2 h }\bigg\rgroup$

⠀⠀⠀⠀⠀Here r is the radii of Cylinder, h is the Height of Cylinder & $\pi = \dfrac{22}{7}$

Therefore,

• Ratio of the Volume of two Cylinder's are :

$\qquad :\implies\:\bf\dfrac{Volume_{(Cylinder\:1)}}{Volume_{(Cylinder\:2)}}=\dfrac{\pi (r_1)\:^2 \:h_1}{\pi (r_2)\:^2 \:h_2} \:\:$

$\qquad\sf :\implies\:\dfrac{\pi (r_1)\:^2 \:h_1}{\pi (r_2)\:^2 \:h_2} \:\:$

$\qquad \sf:\implies\:\dfrac{\cancel {\pi} (r_1)\:^2 \:h_1}{\cancel {\pi} (r_2)\:^2 \:h_2} \:\:$

$\qquad :\implies\:\sf\dfrac{ (r_1)\:^2 \:h_1}{ (r_2)\:^2 \:h_2} \:\:$

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:Now \: By \: Substituting \: the \: known \: Values \::}}$

$\qquad :\implies\sf\:\dfrac{ (r_1)\:^2 \:h_1}{ (r_2)\:^2 \:h_2} \:\:$

$\qquad :\implies\:\sf\dfrac{2\:^2 \times \:5}{3\:^2 \times \:3} \:\:$

$\qquad :\implies\sf\:\dfrac{4\times \:5}{9 \times \:3} \:\:$

$\qquad :\implies\sf\:\dfrac{20}{27} \:\:$

$\qquad \longmapsto \frak{\underline{\purple{\:Ratio = 20:27 }} }\bigstar$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Ratio \:of\:two\:Cylinder's \:is\:\bf{20:27.}}}}$

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