Question

If the diameter of a wire is decreased by 10%, by how much per cent approximately will the length be increased to keep the volume constant? 

(a) 5% 

(b) 17% 

(c) 20% 

(d) 23%

Answer 1

(d) 23%

Since the wire is cylindrical in shape, its volume = \(\frac14πd^2l\)

where d is the diameter, l is the length. Also

r² = \(\big(\frac{d}{2}\big)^2 = \frac{d^2}{4}\)

Decrease in diameter = d – 10% of d

= d\(\bigg(1-\frac{10}{100}\bigg) = \frac{9d}{10},\) new length = l m. Then, 

New volume = Original volume

= \(\frac{19}{81}\times100\) % = 23% (approx.)