Lateral Thinking Game #2 - The Harder Ones !!

Stoday · Post by **Stoday** » Fri Nov 16, 2007 4:53 pm

Here's my difficult one:

I have a metal sphere. I drill a hole through the centre. The hole is 60mm long. What's the volume of metal that's left?

The volume of a sphere is 2/3 pi r cubed. If I tell you that you can use that formula and express the answer as a multiple of pi, you can work it out in your head.

Stoday · Post by **Stoday** » Fri Nov 16, 2007 4:58 pm

Hoovie wrote:nothing!!! you were right -EXCEPT for the need to travel EAST across interational date line.

to go "back in time", you have to travel WEST!

NO. I was right, you are wrong.

Japan starts its day before the USA. The USA is to the EAST of Japan. You travel EAST over the date line to go back a day.

I will accept a low grovel from you Hoovie.

Hoovie · Post by **Hoovie** » Fri Nov 16, 2007 5:19 pm

not gonna get it, old man!!

the point is you do not have to travel over the international date line to go back to a previous day!!

easy example:

Spain is GMT +1
Portugal is GMT

The Twins mother is at the Spanish side of the border control at 30 minutes past midnight of the 1st March and Stoday(the older twin) pops out.
The car crosses the Border driving WEST into Portugal 10 minutes later and now instead of being 40 minutes past midnight on 1st March, it is 40 minutes past 11pm on 28 February.
Bludall Pops out 5 minutes later.

So Stoday was born 30 minutes PAST Midnight on 1st March, and Bludall wass born 15 minutes later at quarter TO midnight on 28th February

Hoovie · Post by **Hoovie** » Fri Nov 16, 2007 5:20 pm

Stoday wrote:Here's my difficult one:

I have a metal sphere. I drill a hole through the centre. The hole is 60mm long. What's the volume of metal that's left?

The volume of a sphere is 2/3 pi r cubed. If I tell you that you can use that formula and express the answer as a multiple of pi, you can work it out in your head.

Is that a Lateral Thinking Puzzle or just a mathematical question?

Stoday · Post by **Stoday** » Fri Nov 16, 2007 6:07 pm

You can solve it either way. The lateral thinking way is easier because you don't need maths. The mathematical way requires calculus.

Hoovie · Post by **Hoovie** » Fri Nov 16, 2007 6:15 pm

Unless I am missing something obvious, the answer canot be provided with the information given as you do not provide the bore of the hole or the size of the sphere, just the length.

My answer is the volume is the same as I am assuming the bore is infinately small.

Stoday · Post by **Stoday** » Fri Nov 16, 2007 11:51 pm

I have not given the size of the sphere nor the bore of the hole. The bore does not have to be zero diameter. You do have enough information.

Keep thinking

Wood Magnet · Post by **Wood Magnet** » Sat Nov 17, 2007 3:10 am

I was born on the 29th Feb. I have March 1st as my birthday
because i was born after 12pm.
Just thought you would like to know.

Hoovie · Post by **Hoovie** » Sat Nov 17, 2007 9:34 am

Wood Magnet wrote:I was born on the 29th Feb. I have March 1st as my birthday
because i was born after 12pm.
Just thought you would like to know.

Does that mean that you only get proper birthday pressies every 4 years

My Dad was born on 28th Feb in a leap year and I always thought it would have been cool if he was born one day later - then I would be older then him after a few years and could tell him what to do

Hoovie · Post by **Hoovie** » Sat Nov 17, 2007 9:37 am

Stoday wrote:I have not given the size of the sphere nor the bore of the hole. The bore does not have to be zero diameter. You do have enough information.

Keep thinking

If you are not providing any initial volume and am asking for a volume after an action, then the volume left must be zero.

Don't know why, but the answer to the question is ZERO

Stoday · Post by **Stoday** » Sun Nov 18, 2007 4:30 am

Hoovie wrote:
Stoday wrote:
If you are not providing any initial volume and am asking for a volume after an action, then the volume left must be zero.

Don't know why, but the answer to the question is ZERO

No it's not zero. You don't have a volume, but you do have the length of the hole. If there were no volume left, you couldn't have a length of hole.

Do you give in?

Hoovie · Post by **Hoovie** » Sun Nov 18, 2007 9:04 am

No !!

Bludall · Post by **Bludall** » Sun Nov 18, 2007 9:58 am

To calculate the volume of a sphere it's 4/3 pi r cubed.

It's a not a cylinder with flat ends that's removed, it's a straight sided object with spherical ends.

Hoovie · Post by **Hoovie** » Sun Nov 18, 2007 10:31 am

Ah-ha!

Formula corrections are always good

Volume of Sphere is 113 cubic cm before hole

Drilling hole in sphere will effect Mass of sphere, but will not effect volume of sphere so...

Volume of Sphere is 113 cubic cm AFTER hole as I must assume the profile of the sphere is still round and am ignoring the flattening of the ends where the hole was drilled

Stoday · Post by **Stoday** » Sun Nov 18, 2007 2:06 pm

Yes Bludall, the formula is 4/3 pi r³

Hoovie is nearly right. This is the argument:

Stoday said that the length of the hole is sufficient information. Therefore the diameter of the sphere dosn't matter, provided it's more than the length of the hole. You could have a sphere the size of a football and drill a 60mm long hole through it, provided the diameter of the drill is big enough.

Similarly you could reduce the diameter of the hole, provided you also reduce the diameter of the sphere to keep the hole to 60mm long. In the limit, the hole diameter is infinitestimally small and the diameter of the sphere is then 60mm.

Since the volume left must be constant, whatever the diameter of the sphere, this volume must be the same as the 60mm diameter sphere.

That is 4/3 pi 3³ or (4 * 355 * 3 * 3 * 3) / (3 * 113) = 113.097 cu cm.

(355/113) is a useful approximation to pi