Question

The radii of two cylinders are in the ratio of 1:√3. If the volumes of two cylinders be same, find the ratio of their respective heights.​

Answer 1

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Answer 2

GiveN :

• Radius of two cylinders are in ratio of 1:√(3)
• And ratio their volume is same

To FinD :

• Ratio of their heights

SolutioN :

We are given that the ratio two cylinders is 1:√(3). So, let

• Radius of first Cylinder (r1) be 1x
• And radius of second cylinder (r2) be √(3) x

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$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underbrace{\sf{Ratio \: of \: heights}}$

Volume of both the cylinders is same, so equate both the volume

$\implies \sf{Volume_1 \: = \: Volume_2} \\ \\ \implies \sf{\pi r_1 ^2 h_1 \: = \: \pi r_2 ^2 h_2} \\ \\ \implies \sf{\dfrac{\pi r_1 ^2 h_1}{\pi r_2 ^2 h_2} \: = \: 1} \\ \\ \implies \sf{\dfrac{h_1}{h_2} \: = \: \dfrac{r_2 ^2}{r_1 ^2}} \\ \\ \implies \sf{\dfrac{h_1}{h_2} \: = \: \dfrac{(\sqrt{3}x)^2}{1x^2}} \\ \\ \implies \sf{Ratio \: = \: \dfrac{3x^2}{1x^2}} \\ \\ \implies \sf{Ratio \: = \: \dfrac{3}{1}} \\ \\ \underline{\sf{\therefore \: Ratio \: of \: heights \: is \: 3:1}}$