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Question
Two cylinders of same volume have their radii in the ratio 1 : 6, then ratio of their heights is ______.
Solution
Two cylinders of same volume have their radii in the ratio 1 : 6, then ratio of their heights is 36 : 1.
Explanation:
Let r1, r2 be the radii and h1, h2 be the heights of two cylinders.
Given, `r_1/r_2 = 1/6`
Now, according to the question,
`pir_1^2h_1 = pir_2^2h_2` ...[∵ Volume of cylinder = πr2h]
⇒ `r_1^2/r_2^2 = h_2/h_1`
⇒ `(r_1/r_2)^2 = h_2/h_1`
⇒ `(1/6)^2 = h_2/h_1`
⇒ `1/36 = h_2/h_1`
or `h_1/h_2 = 36/1`
or h1 : h2 = 36 : 1
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