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Question
The radius of a wire is decreased to one-third. If volume remains the same, the length will become
Options
3 times
6 times
9 times
27 times
Solution
Let V1 and V2 be the volume of the two cylinders with h1 and h2 as their heights:
Let r1 and r2 be their base radius.
It is given that
`pi r_1^2 h_1 = pir_2^2 h_2`
`V_1 = V_2 " and " r_2 = 1/3 r_1 ⇒ r_1^2 h_1 = (1/3r_1)^2 h_2`
`⇒h_2 = 9h_1`
Hence, the length will become 9 times.
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