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प्रश्न
Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is ______.
उत्तर
Two cylinders of equal volume have heights in the ratio 1 : 9. The ratio of their radii is 3 : 1.
Explanation:
Let r1, r2 be the radii and h1, h2 be the heights of two cylinders.
Given, `h_1/h_2 = 1/9`
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 = 9/1`
⇒ `r_1/r_2 = sqrt(9)/1`
⇒ `r_1/r_2 = 3/1`
Hence, r1 : r2 = 3 : 1
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