Sphere to wire !!!!

We know that when any solid is melted or drawn and given a new shape, the volume remains the same as before.

Let $l$ be the length of the wire.

So, volume of the sphere in metres $=\frac{4}{3} \pi r^{3} = \frac{4}{3} \pi (\frac{18}{2\times 100})^3$

Now, after being drawn into wire, its volume in metres $=\pi r^{2} l= \pi (\frac{4}{2\times 1000})^2 l$

Now, we have $\frac{4}{3} \pi (\frac{18}{2\times 100})^3=\pi (\frac{4}{2\times 1000})^2 l$

$\implies \frac{4}{3} \pi \times \frac{18}{200} \times \frac{18}{200} \times \frac{18}{200}=\pi \times \frac{4}{2000} \times \frac{4}{2000} l$

On evaluating, we finally get, $l=9\times 3\times 9 = \boxed{243}$

So, we get the length of the wire $=l=\boxed{243}$

volume of sphere = volume of wire

Volume of sphere= 4/3 πR^3, Volume of cylinder= πr^2 h, When a sphere is turned into a wire then the wire act like a cylinder. So here we have radius of sphere,R = 18/2=9 cm Radius of wire, r = 4/2=2 mm= 0.2 cm So , volume of sphere= Volume of cylinder Or, 4/3 πR^3 = πr^2 h Or, 4/3 π〖(9)〗^3 = π〖(0.2)〗^2 h Or, h= 243 m

vol. of sphere=vol. of cylinder; 4/3(pi)r^3=pi(R^2)h ; where, r=radius of the sphere,r=radius of sphere & h=height of the cylinder i.e,length of the wire 4/3(3.14)(0.09^3)=(3.14)(0.002^2)h so,h=4/3(3.14)(0.09^3)/(3.14)(0.002^2 ) hence,h=243m(sol.)

We know the volume of a sphere is 4/3x22/7xr^3. Therefore the volume of the given sphere is 21384/7. Now the wire is in the form of a cylinder so volume of a cylinder is 22/7xr^2xh. So by the problem 22/7xr^2xh=21384/7. So by solving the equation we get h=243 meters.

The volume of a sphere is $\frac{4}{3}$ \ * pi * r * r* r ) = $\frac{4}{3}$ * pi * 0.09 * 0.09 * 0.09 = 0.000972 pi.

The volume of a cylinder is pi * r * r * h = pi * 0.002 * 0.002 * h = 0.000004h * pi.

Since they are from the same materials, they have the same volume.

Thus, 0.000972 pi = 0.000004h * pi. h = $\frac{0.000972}{0.000004}$ = 243m

The formula for the volume of a sphere is $\frac{4}{3}\pi r^{3}$ .The problem gives us the diameter of the sphere.The radius of the sphere is equal to half of the diameter so $r = \frac{18 cm}{2} = 9 cm$ .So the volume of the copper sphere is $\frac{4}{3} \times \pi \times 9 cm \times 9 cm \times 9 cm = 972\pi cm^{3}$ .

The formula for the volume of a cylinder is $h\pi r^{2}$ where $h$ is the height( in this case the length) of the cylinder and $r$ is the radius of the base.The radius of the copper wire is $\frac{0.4 cm}{2} = 0.2 cm$ .So the volume of the wire is $h\pi 0.04 cm^{2}$ .

Because the entire copper sphere is drawn into the wire,the volume of the sphere must be equal to the volume of the wire.So we get

$972\pi cm^{3} = h\pi 0.04 cm^{2}$

Now we divide both sides by $\pi$ .We get

$972 cm^{3} = 0.04h cm^{2}$

Then we divide both sides by $0.04 cm^{2}$ and we get

$24300 cm = h$

So $h = 24300 cm$ .But the question is asking for the length in meters,so we convert $24300 cm$ to meters and we get $\frac{24300 cm}{100 cm} = 243 m$ .So the answer is $\boxed{243 m}$ .

VOLUME OF SPHERE=4/3 X 22/7 X R^3

VOLUME OF WIRE(VOLUME OF CYLINDER)=22/7 X r^2 X H

VOLUME OF SPHERE=VOLUME OF CYLINDER

4/3 X 22/7 X R^3=22/7 X r^2 X H

4/3 X 9 X 9 X 9=2/10 X 2/10 X H

24300 CM=H

243 METERS=H

volume will remain constant & hence volume of sphere = volume of wire(cylinder)

Volume of sphere = $\frac{4}{3}\pi r^3$

Volume of cylinder = $\pi r^2h$

$\frac{4}{3}\pi r^3$ = $\pi r^2h$

$\frac{4}{3}\pi (0.09)^3$ = $\pi (0.002)^2h$

Divide the $\pi$ of that equation

$\frac{4}{3} \times 0.000729$ = $0.000004 \times h$

$h = \frac {\frac{4}{3} \times 0.000729}{0.000004}$

$h = \frac {0.000972}{0.000004}$

$h= 243$

So the length is $243$

(4xπx0.09^3)/3=πx0.002^2xh

h=243m

V_sphere = V_wire ---> 4/3.phi.(180/2)^3 = phi.(4/2)^2.h ---> 4/3 . 729000/3 = 4 .h ----> 729000/3 [mm]= h ----> h = 243000/1000 [m] = 243 m. Answer : 243 . HAPPY CHRISTMAS DAY

The volumes of the sphere and the wire have to be equal, since the same material is used for both. The volume of a sphere of radius $r$ is $\dfrac{4}{3}\pi r^{3}$ while the volume of a wire (which is in fact a very thin cylinder) is given by $\pi r^{2}{l}$ , where $r$ is the radius of the wire and $l$ is its length.

Converting all given lengths to centimeters (for convenience):

$V_{sphere} = \dfrac{4}{3}\pi \left(\dfrac{18}{12}\right)^{3} = 972\pi$

$V_{cylinder} = \pi \left(\dfrac{0.4}{2}\right)^{2}l = 0.04\pi l$

$\Rightarrow 0.04\pi l = 972 \pi$

$\Rightarrow l = 24300 cm = \boxed{243 m}$

Volume of Sphere= 4/3 (pi)(r^3)=4/3(pi)(0.09)^3

Length of Wire=(4/3(pi)(0.09)^3) / ((pi)(0.002)^2)=243m