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Question
The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is ______.
Options
10 : 17
20 : 27
17 : 27
20 : 37
Solution
The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is 20 : 27.
Explanation:
Let the radius of first cylinder be 2x and second cylinder be 3x.
The height of first cylinder be 5y and second cylinder be 3y.
Now volume of first cylinder be `pi xx (2 xx x)^2 xx 5 xx y`
And volume of second cylinder be `pi xx (3 xx x)^2 xx 3 xx y`
Thus ratio = `(pi xx (2 xx x)^2 xx 5 xx y)/(pi xx (3 xx x)^2 xx 3 xx y)`
= `20/27`
Thus the ratio is `20/27`.
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