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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

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20 : 27

20 : 21

21 : 27

27 : 20

answer is A.

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Detailed Solution

Given- ratio of radii of two cylinders =

2 : 3

Heights are in the ratio of 5: 3.
Let common ratio for radii is r, common ratio for heights is h.

r 1 = 2 r r 2 = 3 r h 1 = 5 h h 2 = 3 h V o l u m e = π r 2 h V = π (2 r) 2 5 h π (3 r) 2 3 h V = 20 r 2 h 27 r 2 h V = 2027 So, 20 : 27

Thus, the ratio of their volumes is

20 : 27

.
Hence, option 1 is the correct option.

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