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प्रश्न
The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.
उत्तर
Let the radii of the cylinders be r1 and r2 and their heights be h1 and h2 .
We have,
`"r"_1: "r"_2 = 2 : 3 or "r"_1/"r"_2 = 2/3` ...........(i)
and `"h"1 : "h"2 = 5 : 3 or "h"_1 /"h"_2 = 5/3 ........(ii)`
Now,
The ratio of the volumes of the cylinders `="Volume of the first cylinder"/"Volume of the second cylinder"`
`= (pi"r"_1^2"h"_1)/(pi"r"_2^2"h"_2)`
`= (("r"_1)/"r"_2)^2xx"h"_1/"h"_2`
`= (2/3)^2xx5/3` [Using (i) and (ii)]
`=20/27`
= 20 : 27
So, the ratio of the volumes of the given cylinders is 20 : 27.
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