Question

1cm^3 of gold is drawn into a wire 0.1mm in diameter. Find the length of the wire​

Answer 1

Step-by-step explanation:

1cm =10mm1cm=10mm

Cubing both sides:

1cm^3=1000mm^31cm

3

=1000mm

3

Volume of cylinder = \pi r^2hπr

2

h , where r=radius and h= height.

Given the diameter of the wire is 0.1mm

Radius= \frac{Diameter}{2}= \frac{0.1}{2}=0.05Radius=

2

Diameter

=

2

0.1

=0.05

And, volume of gold = volume of wire= 1000mm^3mm

3

Therefore, we have:

Volume =\pi r^2hπr

2

h

Plug in the known values, volume=1000, r=0.05 and \pi = \frac{22}{7}π=

7

22

:

1000= \frac{22}{7}(0.05)^2h1000=

7

22

(0.05)

2

h

1000= \frac{22}{7}*0.0025*h1000=

7

22

∗0.0025∗h

Multiply both sides by 7:

1000*7=0.055*h1000∗7=0.055∗h

Divide both sides by 0.055:

\frac{7000}{0.055}=h

0.055

7000

=h

h=127272.73h=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)

1000

127272.73

=127.27m(approx)

Therefore, length of wire = h = 127272.73mm =127.27m

Answer: 127272.73mm or 127.27m