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The radius of a wire is decreased to one - third and its volume remains the same. The new length is how many times the original length?
We know that wire is in the shape of a cylinder.
So, the volume of wire = $$\pi\ r^2h$$
$$\pi\ r^2h_1$$ = $$\pi\ (\frac{r}{3})^2h_2$$
Cancelling π on both sides,
$$\ r^2h_1$$ = $$\frac{\ r}{9}^{^2}h_2$$
$$9h_1$$ = $$h_2$$
length is increased by 9 times
D is the correct answer.
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