Question

1 (cm) 3 of gold is drawn into a wire 0.1 mm in diameter find the length of the wire

Answer 1

[tex]1cm =10mm [/tex]
Cubing both sides:
$1cm^3=1000mm^3$
Volume of cylinder = $\pi r^2h$, where r=radius and h= height.
Given the diameter of the wire is 0.1mm
$Radius= \frac{Diameter}{2}= \frac{0.1}{2}=0.05$
And, volume of gold = volume of wire= 1000$mm^3$
Therefore, we have:
Volume =$\pi r^2h$
Plug in the known values, volume=1000, r=0.05 and $\pi = \frac{22}{7}$:
$1000= \frac{22}{7}(0.05)^2h$
$1000= \frac{22}{7}*0.0025*h$
Multiply both sides by 7:
$1000*7=0.055*h$
Divide both sides by 0.055:
$\frac{7000}{0.055}=h$
$h=127272.73$

1m = 1000mm
To convert mm into meter, we have to divide  number of mm by 1000.

127272.73mm = $\frac{127272.73}{1000} =127.27m(approx)$
Therefore, length of wire = h = 127272.73mm =127.27m

Answer: 127272.73mm or 127.27m
 

Answer 2

Solution:-

1 Volume of the gold = 1 cu cm
1 cu cm = 1000 mm
Diameter of wire = 0.1 mm 
Radius of wire = 0.1/2 = 0.05 mm
Now,
Volume of the gold in wire = volume of the gold
Volume of the gold in the wire = 1 cu cm = 1000 mm
⇒ 22/7*0.05*0.05*h = 1000
⇒ 0.055h = 7000
⇒ h = 7000/0.055
⇒ h = 127272 mm
Or
127272/1000
Length of the wire = 127.272 m
Answer.