Question

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

Answer 1

diametre be d
radius be d/2
vol=πr*r*h
    =πd*d*h/4
if d is  increased by 5% then d- 5%of d
d-5/100*d
d-d/20
19d/20
∴r=2*19d/20=19d/40
vol=πd*d*h/4
π*19d/40*19d/40*h
∴h=400d/361 ( calculate the above one)
increase in length=400h/361-l
=39l/361
%of increase =39h/361/h*100=3900/361% =10.80%

Hope This Helps :)

Answer 2

Given:

Diameter of cross section of wire is decreased by 5%

To find: How much % will the length be increased so that its volume remains same.

Let

Diameter = d

Radius = d/2

Volume = πr*r*h

             = πd*d*h/4

Given that, d is decreased by 5%, So, d - 5% of d

=> d-5/100*d

=> d-d/20

=> 19d/20

                   ∴ r = 2*19d/20

                         = 19d/40

Volume = πd*d*h/4

             => π*19d/40*19d/40*h

             ∴ h = 400d/361

Now,

Increase in length  = 400h/361-l

                                = 39l/361

%of increase             =  39h/361/h*100

                                 = 3900/361%

                                 = 10.80%

Therefore, 10.80% of length should be increased, so volume will remain same.