Unusual/Astonishing facts post....

[TedLaRue]

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.

The size of the sphere is not determined by the 1" height. A large diameter hole drilled through a large sphere might leave a 1" tall ring, just as a smaller hole drilled through a smaller sphere leaves a 1" tall ring.

The interesting fact is that the volume of the remaining ring is the same no matter what the size of the original sphere. With a large hole in a large sphere, the thickness of the 1" tall ring would be less because there's less curvature. This compensates for the larger diameter ring.

The volume of a sphere is 4/3 pi r^3, but computing the volume of the remaining ring is not easy.

 

[jdbower]

The volume of a sphere is 4/3 pi r^3, but computing the volume of the remaining ring is not easy.

Here's a hint for the mathematically inclined...

Here's an astonishing fact, I actually remember enough high school geometry and algebra to solve some of these things

 

[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.

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

0.817 oz.
larry

 

[tallyho8]

The size of the sphere is not determined by the 1" height. A large diameter hole drilled through a large sphere might leave a 1" tall ring, just as a smaller hole drilled through a smaller sphere leaves a 1" tall ring.

The interesting fact is that the volume of the remaining ring is the same no matter what the size of the original sphere. With a large hole in a large sphere, the thickness of the 1" tall ring would be less because there's less curvature. This compensates for the larger diameter ring.

The volume of a sphere is 4/3 pi r^3, but computing the volume of the remaining ring is not easy.

I hope you aren't going to tell us that you gave us a riddle that you don't have the answer to.

 

[TedLaRue]

Originally Posted by 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.)

SPYDERLK's answer of 0.817 oz. matches mine. I posted the puzzle only because I thought it was interesting that the diameter of the ball didn't matter.

To actually solve the problem requires knowledge of higher math (usually the second semester of Calculus) unless someone posted a formula on the Web somewhere. There were so many correct answers to my previous puzzle that I thought I'd post a harder one.

As others have posted previously, the knowledge behind the collective membership of this forum is quite broad.

 

[TedLaRue]

I hope you aren't going to tell us that you gave us a riddle that you don't have the answer to.

And for you, Mr. Smart Guy, you can stay after school today and answer this:

How are an ocean wave, a sunflower blossom, a pentagon, the painting "The Last Supper", a snail, and pine cone related? Your belly button might also be related, but that's debatable.

 

[tallyho8]

And for you, Mr. Smart Guy, you can stay after school today and answer this: How are an ocean wave, a sunflower blossom, a pentagon, the painting "The Last Supper", a snail, and pine cone related? Your belly button might also be related, but that's debatable.

 

[higgy]

Ok, the I was incorrect with the diameter being fixed, however it is exactly the cylinder with the the curvature on the ends that I was speaking to that gives the difference in the volume.

 

[higgy]

well the sun flower and the pine cone both follow the Fibonacci sequence.

This is an example of a recursive sequence, obeying the simple rule that to calculate the next term one simply sums the preceding two:


F(1) = 1
F(2) = 1
F = F(n 1) + F(n 2)

 

[TedLaRue]

higgy,

Yes, the other things you said in your post were right on the money, including your descriptions of the ring and the part that is "drilled out". You guys are good at visualizations.