I was really looking forward to seeing a cool trick at the end of this, but alas, it was but a farce.

What a waste.

 

I don't believe Archimedes discovered this ratio. I think it is much older. But he knew it to be true because of water displacement. Displacement proves the ratio. He tried several ways to mathematically and geometrically prove it. Records and students indicate this. There were many forms of customized "calculus" at the time. Such as using radii as levers(triangles) and many sided polygons. Many more configurations I'm sure.

Every empire had it's pi and calculus for it.

 

In determining the answer to the question below, you do not know the value of pi and cannot use the formula for the volume of a sphere, or the formula for the area of a circle.

I have a solid steel sphere, 600mm in diameter and a machine that can convert the sphere into a single length of wire, with no wastage of material.
The produced wire has the same density as the original sphere.

I have set the machine to produce a wire of 1mm in diameter - exactly how long is the 1mm diameter wire, produced from the 600mm diameter steel sphere?

In giving your answer show your working.

Hello,

This sounds like an extrusion process. You have a lump of material of a given volume and it is extruded into a different shape, in this case a thin wire. It doesnt matter what shape the original material is to start with really, at least in theory. The fact that it is just a known shape and size tells us the volume at the start and at the finish.

 

Hello,

This sounds like an extrusion process. You have a lump of material of a given volume and it is extruded into a different shape, in this case a thin wire. It doesnt matter what shape the original material is to start with really, at least in theory. The fact that it is just a known shape and size tells us the volume at the start and at the finish.

How does it tell you the volume at that start and finish if you are prohibited from using or deriving any formula that directly or indirectly yields the volume either before or after?

 

How does it tell you the volume at that start and finish if you are prohibited from using or deriving any formula that directly or indirectly yields the volume either before or after?

Hello,

Weigh it Are we allowed to weigh it?

I was just commenting on the process itself, not really addressing the actual trick question. In other words, what would this process be like in the real world. In the real world we would know the volume. I assumed the solution was already found after all these replies and i think i saw it in one reply.

 

Hello,

Weigh it Are we allowed to weigh it?

I was just commenting on the process itself, not really addressing the actual trick question. In other words, what would this process be like in the real world. In the real world we would know the volume. I assumed the solution was already found after all these replies and i think i saw it in one reply.

Would weighing it be of any help? I don't think so, not unless you are allowed to weigh a known length of the finished wire.

 

This is driving me crazy.

 

This is driving me crazy.

Did you not read the ‘answer’?