The diameters of two cylinders are in the ratio 3:2 and their volumes are equal. the ratio of their heights is
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Solution :-
The ratio of the diameters of the cylinders = 3 : 2
⇒ The ratio of the radius of the cylinders will be = 3 : 2
Therefore, let the radii of the two cylinder be 3x and 2x respectively.
Let the height of the cylinder be h1 and h2.
Now, Volume of first cylinder = Volume of the second cylinder
i.e. π(3x)²h1 = π(2x)²h2
h1/h2 = (π*4x²)/(π*9x²)
h1/h2 = 4/9
h1 : h2 = 4 :9
So, ratio of their heights is 4 : 9
Answer.
The ratio of the diameters of the cylinders = 3 : 2
⇒ The ratio of the radius of the cylinders will be = 3 : 2
Therefore, let the radii of the two cylinder be 3x and 2x respectively.
Let the height of the cylinder be h1 and h2.
Now, Volume of first cylinder = Volume of the second cylinder
i.e. π(3x)²h1 = π(2x)²h2
h1/h2 = (π*4x²)/(π*9x²)
h1/h2 = 4/9
h1 : h2 = 4 :9
So, ratio of their heights is 4 : 9
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