Question

A steel sphere of radius 4 cm is drawn into a wire of diameter 4 mm. find the length of wire.

Answer 1

Answer:

The length of the wire =2133 cm

Step-by-step explanation:

It is given that a steel sphere of radius 4 cm is drawn into a wire of diameter 4 mm

The volume of sphere is equal to volume of wire

To find the volume of sphere

Equation of  volume of sphere, $V=\frac{4pir^{3} }{3}$

r = 4cm

$V=\frac{4pi*4^{2} }{3}$

$V=\frac{256}{3}$ π

To find the volume of wire

A wire is like a cylinder.

here radius of the wire = 2mm = 0.2 cm

Volume of cylinder $V=pi*r^{2}l$

$V=pi*0.2^{2}l$

V= 0.04xlxπ

To find Length of wire

Volume of sphere and volume of wire are equal

$0.04xl$π$=\frac{256}{3}$  π

$l=\frac{256}{3*0.04}$

Length of wire l = 2133.33≈2133 cm

Answer 2

Answer:

Step-by-step explanation:

According to the question,

Radius of the steel sphere = 4cm.

Now the the sphere is drawn into a wire of diameter 4 mm = 0.4cm.

Irrespective of the diameter the volume of both sphere and wire will remain the same.

Therefore, volume of sphere = (4/3)$\pi$r³ where r is the radius.

or, Volume of the sphere = (4/3)$\pi 4^{3}$

Similarly volume of wire = $\pi$ r²h, where r and h are the radius and length of the wire.

r=d/2 = 0.4/2 = 0.2

So, (4/3) * (22/7) * 4³ = (22/7) * (0.2)² * h

or, h = 2133.34 cm [Ans]