The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm.

Question:

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is
(a) 12 m
(b) 18 m
(c) 36 m
(d) 66 m

Solution:

(c)  36 m
Let h m be the length of the wire.
Volume of the sphere = volume of the wire

$\Rightarrow \frac{4}{3} \pi \times 3^{3}=\pi \times(0.1)^{2} \times h$

$\Rightarrow h=\frac{4 \times 9}{0.001}$

$=3600 \mathrm{~cm}$

$=36 \mathrm{~m}$

 

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