Question

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

Answer 1

Answer:

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Answer 2

Answer:

10.8%

Step-by-step explanation:

volume of wire is given by =$\pi r^{2}l$

where r=radius of wire

          l= length of wire

when diameter is decreased by 5% than new diameter is =d'

d'= d- 5% of d

d'=$d-\frac{5d}{100}$

$d'=\frac{95d}{100}$

as given in the question ,volume remains same

therefore,old volume = new volume

                  $\pi r^{2}l =\pi r'^{2}l'$

       $\pi \frac{d^{2}}{4}l = \pi \frac{d'^{2}}{4}l'$          (∵2r=d)

                    l'=1.108l

hence ,

percentage increased in length =$\frac{l'-l}{l}\times 100$

                                               = $\frac{1.108l-l}{l}\times 100$

                                               = $10.80$