Question

Volume of two cylinders is same. If the ratio of their radii is 2:3 then the ratio of their heights is

______.
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Answer 1

The areas of circles, when compared, is in direct proportion to the squares of their diameters (or radii, as long as you compare radius with radius, diameter with diameter), so, taking your radii of ratios 2:3, the areas of the circles (the sections of the cylinders) would be 2^2:3^2, or 4:9. since the cylinder lengths are the same, the ratios remain the same.

You could have performed a few calculations yourself, though to find this out, by calculating the areas of circles with radii (or diameters) 2and 3, 6 and 4, and 9 and 6, for instance, and working out the ratios, which in all cases would be 4:9, or for simplicity’s sake, reverse the comparison Larger:smaller, which gives a ratio of 2.25:1