Given:
44 cu. cm of wire is drawn into a wire of diameter 2 mm.
To find:
The length of the wire.
Solution:
We know that,
1 cm = 10 mm
1 cu. cm = 1000 cu. mm
We have, a wire of cylindrical shape.
Volume of the wire = 44 cu. cm
= 44000 cu. mm
Radius of the wire = 2 mm
Volume of a cylinder is:
![V=\pi r^2h](https://img.qammunity.org/2022/formulas/mathematics/high-school/epjh35sj5an0p978o7hjzs2ufmx9ct9m3d.png)
Where, r is the radius and h is the height.
Putting V=44000,
and r=2, we get
![44000=(22)/(7)* 2^2* h](https://img.qammunity.org/2022/formulas/mathematics/high-school/f86kfcn931dtpftufg4uq2fw4nvyggz1bp.png)
![44000* (7)/(22)=4h](https://img.qammunity.org/2022/formulas/mathematics/high-school/6eirk77g28dd5c6bkxjtblcbnwqrya7pjm.png)
![14000=4h](https://img.qammunity.org/2022/formulas/mathematics/high-school/6g12rusvwd4br2wf9bm4radw7rd4ctg51c.png)
Divide both sides by 4.
![(14000)/(4)=h](https://img.qammunity.org/2022/formulas/mathematics/high-school/w4o7ems29qgndl607fuvmxukcwhwqynfim.png)
![3500=h](https://img.qammunity.org/2022/formulas/mathematics/high-school/ift16kt2rfvspf9kt58maxukf7ucqrhsna.png)
Therefore, the length of the wire is 3500 mm or 350 cm.