The diameter of a sphere is 42 cm.


The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.



Diameter of sphere $=42 \mathrm{~cm}$

Radius of sphere $=21 \mathrm{~cm}$

Volume of sphere $=\frac{4}{3} \pi r^{3}=\frac{4}{3} \pi \times 21 \times 21 \times 21 \mathrm{~cm}^{3}$

Diameter of wire $=2.8 \mathrm{~cm}$

Radius of wire $=1.4 \mathrm{~cm}$

Let the length of the wire be $/ \mathrm{cm}$.

Volume of the wire $=\pi r^{2} l=\pi \times 1.4 \times 1.4 \times 1$

The volume of the sphere is equal to the volume of the wire. 

$\pi \times 1.4 \times 1.4 \times l=\frac{4}{3} \pi \times 21 \times 21 \times 21$

$l=\frac{4 \times 21 \times 21 \times 21}{3 \times 1.4 \times 1.4}=6300 \mathrm{~cm}=63 \mathrm{~m}$

So, the wire is 63 m long.


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