If the diameter of cross-section of a wire is decreased by 5% , by how much percent should the length be increased so that the volume remains the same?

Explanation

given , new`d(1-5/100) = 0.95d`

volume of wire =`pi r^2 l`

`= pi (d^2/4)l= pi/4 d^2 l`

volume of wire =`pi r^2 l'`

`= pi xx (0.95 d/2)^2 l'`

`= pi/4 xx 0.90 xx d^2 l'`

volume of wire initial = volume of wire final

`pi/4 d^2 l = pi/4(0.90)d^2l'`

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