Question

two circular cylinder of equal volumes
have their heights in the ratio 1:2
I find the ratio of their radius​

Answer 1

Answer:

Step-by-step explanation:

We know that the volume of a right circular cylinder with radius r and height h is $$V=πr^2h$$.

It is given that the ratio of the heights of two circular cylinders is 1:2 that is h2​h1​​=21​, therefore,

$$V_{ 1 }=V_{ 2 }\\ \Right arrow πr^{ 2 }_{ 1 }h_{ 1 }=πr^{ 2 }_{ 2 }h_{ 2 }\\ \Right arrow \cfrac { r^{ 2 }_{ 1 } }{ r^{ 2 }_{ 2 } } =\cfrac { { h }_{ 2 } }{ { h }_{ 1 } } \\ \Right arrow \cfrac { r^{ 2 }_{ 1 } }{ r^{ 2 }_{ 2 } } =\cfrac { 1 }{ \frac { { h }_{ 1 } }{ { h }_{ 2 } } } \\ \Right arrow \cfrac { r^{ 2 }_{ 1 } }{ r^{ 2 }_{ 2 } } =\cfrac { 1 }{ \cfrac { 1 }{ 2 } } \\ \Right arrow \left( \cfrac { r_{ 1 } }{ r_{ 2 } } \right) ^{ 2 }=2\\ \Right arrow \frac { r_{ 1 } }{ r_{ 2 } } =\sqrt { 2 }$$

Answer 2

Answer:

Step-by-step explanation:

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