If the diameter of cross-section of a wire is decreased by 20%. How much percent should the length be increased,so that the volume remains the same ?

Expert Answers

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Since the shape of wire is cylindrical, you may evaluate its volume using the following formula, such that:

`V = pi*d^2/4*l`

d represents the diameter of cross section of wire

l represents the length of wire

Since the new diameter of cross section of wire is `d_1 = d - ` `20/100*d` , you need to substitute in equation of volume, such that:

`V = pi*(d_1^2)/4*l_1 => pi*d^2/4*l = pi*(d_1^2)/4*l_1`

Reducing duplicate factors yields:

`pi*d^2/4*l = pi*d^2(1 - 20/100)^2/4*l_1`

Reducing duplicate factors yields:

`l = (1 - 20/100)^2*l_1 => l_1 = l/(1 - 20/100)^2`

`l_1 = l*(100/80)^2 => l_1 = l*(5/4)^2 => l_1 = 1.56*l =>l_1 = 156/100*l = 156%*l`

Hence, evaluating the number of percents the original length of wire needs to be increased, under the given conditions, yields `l_1 = 156%*l.`

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