Question 126

The radius of a wire is decreased to one third. If volume remains the same, length will increase by:

Solution

Let radius of wire is $$r=3$$ cm and length = $$h=1$$ cm

=> Volume of cylinderical wire = $$\pi r^2h$$

= $$\pi\times(3)^2\times1=9\pi$$ $$cm^2$$

New radius = $$r'=\frac{1}{3}\times3=1$$ cm

Let new length = $$h'$$ cm

If volume remains the same, => $$\pi (r')^2\times(h')=9\pi$$

=> $$(1)^2\times(h')=9$$

=> $$h'=9$$

$$\therefore$$ Length was increased by = $$\frac{h'}{h}=9$$

=> Ans - (D)

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