1.

The radius of a wire is decreased to one-third. If volume remains the same, length will increase by :1). 1.5 times2). 3 times3). 6 times4). 9 times

Answer»

Let the initial radius and length of the wire be R and l respectively.

Now, radius changes to r/3, let the new length be $(\;{l_1})$.

? Volume does not change,

$(\PI {r^2}l = \pi {\left( {\frac{r}{3}} \RIGHT)^2}{l_1})$

⇒ $({r^2}l = \frac{{{r^2}}}{9} \times {l_1})$

⇒ l1 = 9l

∴ Length is increased by 9 times.


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