Question

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is
A.12 m
B.18 m
C.36 m
D.66 m

Answer 1

Hint: To get the length of the converted wire can be calculated by equating the volume of sphere and the cylinder (wire). Here the volume of sphere and wire will be same because all the material of the sphere is converted into wire.

Complete step-by-step answer:
Given the diameter of the sphere is 6 cm
As shown in the diagram below AB is the diameter of the sphere having center O

So its radius $ = \dfrac{6}{2} = 3 $ cm
We know the volume of a sphere $ = \dfrac{4}{3}\pi {r^3} $
On putting the value of the radius of the sphere
We get,
Volume of sphere $ = \dfrac{4}{3}\pi {(3)^3} $ cm
Similarly we know the volume of cylinder $ = \pi {r^2}h $
Here the converted wire can be treated like cylinder
Suppose the length of the wire is h cm
And the diameter of the wire is given which is 2mm
So the radius of the wire $ = \dfrac{2}{2} = 1 $ mm or 0.1cm
Then the volume of wire $ = \pi {(0.1)^2}h $
Now we know that the volume of wire and the sphere will be same
That means
 $ 4{(3)^2} \pi= \pi {(0.1)^2}h $
On cancelling out the pie from each side we get,
 $ 4{(3)^2} = {(0.1)^2}h $
On simplifying we get
The value of $ h = 3600 $ cm
On converting cm to m
We get h=36 m.
Hence the length of the wire is 36 m
So, the correct answer is “36 m”.

Note: In this problem to find the volume of wire we have used the volume formula of the cylinder because the wire is treated as a cylinder. Whose length can be assumed as the height of the cylinder.