Unusual/Astonishing facts post....

[tallyho8]

Ted,Can you please explain the metal band riddle. I guess I am a little slow Why doesn't the circumference matter? Lets scale it down. Lets say we are adding 3.2 inches (instead of 32 feet). and to a band that is around my tractor tire which has a circumference of 150 inches vs. my lawnmower wheel which has a circumference of 12 inches, the answer would be the same?

The reason the circumference doesn't matter is because anytime you add 32 feet circumference to a circle it adds about 10 feet (+) to the diameter. If you have a water storage tank in your yard that is 10' diameter and you make a fence in a circle around it that has 32' more circumference than the tank, then the fence will be about 10' more diameter (20'), or about 5' more on each side.

If you add 3.2' to the circumference it will always add about 1' to the diameter and if you add 3.2" to the circumference it will always add about 1" to the diameter.

This same principle applies if your tank is 100', 1000000000000000' or 1'.

 

[TedLaRue]

Erik,

While I was typing up a reply, cp1969 posted a good mathematical explanation. So I'll post only a less mathematical explanation:

EDIT: Dang! While I was typing this up, tallyho8 posted what I was going to say! You guys are good!

The number PI is the ratio of the circumference of a circle to the diameter of the circle. In other words, if you divide the measure of the circumference of any circle by its diameter, you'll always get about 3.1415926 (or PI).

For every inch you add to the diameter, you'll add about 3.14" to the circumference. Put another way, for every 3" you add to the circumference, you'll add about 1" to the diameter. It doesn't matter what the original diameter was. So if you add 30 feet to the circumference, the diameter will go up by about 10 feet.

 

[TedLaRue]

Suppose you have a solid sphere of aluminum. You drill a large hole through the center of it, leaving a ring (sort of like the ball in the end of the lift arms on your 3 point hitch, or the ring in a compression fitting for plumbing). When you lay the ring flat on the table, it is one inch tall.

How much does the ring weigh? (Aluminum weighs 1.56 ounces per cubic inch.)

 

[KYErik]

Thanks cp1969 and Ted and Tallyhoe for the explanation, it makes sense now. I should have pulled out a calculator and checked my work

 

[tallyho8]

Suppose you have a solid sphere of aluminum. You drill a large hole through the center of it, leaving a ring (sort of like the ball in the end of the lift arms on your 3 point hitch, or the ring in a compression fitting for plumbing). When you lay the ring flat on the table, it is one inch tall.

How much does the ring weigh? (Aluminum weighs 1.56 ounces per cubic inch.)

I guess I'm a little to tired to figure out the weight right now but I bet the weight is the same no matter the size of the sphere, 1' or 100'.

 

[BTDT]

Weighs the same as a piece of chewed up wonder bread?

 

[RobertN]

Weighs the same as a piece of chewed up wonder bread?

Without extra moisture from a drink of water or other liquid, the soft white bread turns leaves you with cotton mouth, and turns in to a gummy ball that is hard to chew and swallow. I've had about 15 people try it, and made a buck on the bet every time.

 

[Lloyd_E]

You can not fold a piece of paper more than 7 times.

Try it...

Lloyd

 

[higgy]

na, it is not the same depending on the size of the ball, the hint is that it is one inch off the table, leaving a cross section that would be roughly d shaped that is contiguous across 360 degrees, That will give you a volume that then can be converted to a weight. When you drilled through the center you eliminated a cylinder of material with a radius on each end.

Calculate it out and get the answer. The size of the sphere is fixed by the 1" hight after removal of the material.

 

[SPYDERLK]

Suppose you have a solid sphere of aluminum. You drill a large hole through the center of it, leaving a ring (sort of like the ball in the end of the lift arms on your 3 point hitch, or the ring in a compression fitting for plumbing). When you lay the ring flat on the table, it is one inch tall.

As much as a 1" ball of Al, I guess.
larry
ps -- so, as I recall, 4/3 pi r cubed x the density?