Question

If diameter of coss section of a wire is decreased by 5% how much percent will the height should be increased so that the volume be the same

Answer 1

Sol:
Let the diameter of the cross section of the wire = d cm
Volume of the wire = πr2h
= 22/7 x d2/4 x h
= 11/14 x d2 x h1
Decreased diameter of the wire = 0.95 d
Volume of the wire = πr2h
= 22/7 x (0.95 d)2/4  x h2
= 11/14 x (0.95 d)2 x h2

11/14 x d2 x h1 = 11/14 x (0.95 d)2 x h2
d2 x h1 = 0.95 x d2 x h2
h1 = 0.95 h2
Increase in length = h2 - h1
= h2 - 0.95 h2
= 0.05 h2
Percentage increase in the length of the wire = [(h2 - h1) / h1] x 100
= [(h2 - 0.95 h2) / 0.95 h2] x 100
= 5.26 %






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