Bharati S
from Dr.M.S.Udayamurthy School of Excelence (C.B.S.E), Namakkal,, asked a question

Subject: Math
, asked on 14/10/09
If the diameter of the cross section of the wire is decreased by 5%,how much %will the length be increased so that the volume remains the same

Suresh Anand
From D.a.v. Boys Senior Secondary School, added an answer, on 6/2/12

398 helpful votes in Math
V = pi.h.r^2 (cylinder)

When diameter is decreased by 5%, radius also is decreased by 5%. So new radius is 19r/20.

So V becomes pi.h.(19r/20)^2 = pi.h.(361r^2)/400.

But you want to maintain the volume at a constant, so h is to be multiplied by 400/361 to keep it constant.

So length is to be incresed by 400/361 - 1 = 39/361 times, i.e. 39 x 100/361 = 10.8033 %

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