Question

ratio of height of two cylinder with equal radii is 5:9 then ratio of their volume is

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Answer 1

Answer:

Volume of cylinder=πr²h

ratio of volume of cylinder=πr²5/πr²9

= 5/9

ratio of volume of cylinder=5:9

Answer 2

Given

• Ratio of height of two cylinders with equal radii is 5:9.

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To find

• Ratio of their volume.

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Solution

• As it is given in the question that radius of their cylinder are equal.

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Let us take their radii be r.

Now, let the ratio of their height be x.

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$\tt\longrightarrow{height_1 (h) = 5x}$

$\tt\longrightarrow{height_2 (H) = 9x}$

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• Formula used

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$\: \: \: \: \: \: \: \boxed{\bf{\bigstar{Volume_{(Cylinder)} = \pi r^2h{\bigstar}}}}$

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$\: \: \: \: \: \: \: \: \: \:\underline{\sf{\red{Finding\: the\: ratio}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Ratio = \dfrac{\pi r^2 h}{\pi r^2H}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Ratio = \dfrac{\cancel{\pi} \times \cancel{r^2} \times 5x}{\cancel{\pi} \times \cancel{r^2} \times 9x}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Ratio = \dfrac{5x}{9x}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Ratio = \dfrac{5}{9}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {Ratio = 5:9}$

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Hence,

• Ratio of their volumes is 5:9.