Here's a maths one for ya

[gasbanni]

I don't have the formula to calculate it

Well done Sherlock!

Plonker can you read ? It can be worked out by plotting, but I dont have the forumla, but know how to do it !

 

[gasbanni]

Its simply a pyramid with three flat faces and one concave curved face, we have a chord intersecting the pyramid.

The drawing boards Ive previously referred to were 8' long and 5' high equipped with a parallel arm and went up hydraulically.
On one of these the shape could be scaled drawn exactly, projected and plotted and very accurately calculated using a planometer.

Given that equipment the answer would probably take half a day to work out ! or maybe a bit longer. !

 

[gasbanni]

Been a bit busy but estimate is 950cm³ (volume of a cylinder removed of radius 1cm, length approximately √300 cm, being approx 50cm³) , will work out later. Got the method/shape in my head, doesn't need calculus; pythagoras is as hard as it gets.

If I get it wrong I shall remember to take Freddies lead and blame my tool, which in my case will be a pen and paper.

since when did pythagoras take into account arcs ?

Well...

What I said was that pythagoras was 'as hard as it gets'.

And in any event, Pythagoras is more than just a simple equation, it can be used to derive all sorts of things, including stuff that includes arcs. The beauty of such a simple equation is it's power.

Pythagoras can be used to calculate the radius of the inscribed circle of a triangle, and also the radius of the circumscibed circle of a triangle.

http://en.wikipedia.org/wiki/Equilateral_triangle#Principal_properties

Both these calculations need to be made to solve this problem. The two circles are key to working out the height of that strange shape you go on about. The location of the excircle also allows us to calculate the amount of wood lost as the drill penetrates the square at the corner.

(I don't think it's an equilateral triangle but the principle applies, still pythagoras)

Once you have worked out the height (h) of the shape, you need to calculate the area of the base (that's the incircle plane worked out previously) of your funny shape. The area of the base is simply the area of the triangle at that plane minus the csa of the drill bit. As there are three funny shapes you divide that answer by three, giving a.

You then apply the standard formula for the volume of a cone. base x height / 3 or in our example ah/3

That's the hard part done.

Then a bit more simple geometry and bob's your uncle.

All pythagoras apart from calculating the area of a circle (drill bit), you just need to break the square down into a load of right angle triangles to work it out.

Wrong its harder than Pythagoras there isn't a right angle triangle involved in working this out. Why on earth quote wikipedia on equilateral triangles ???? that has no bearing on solving this problem !!!

 

[freddiemercurystwin]

Haha, so much BS in this thread, yea yea you boast you can do it but actually you can't that's why you've not done it. Of course, you need a special drawing board to do it! How convenient!

 

[chapeau]

There are several right angled triangles involved if you want to get the answer.

Well Freddie your attempt was embarrasingly wrong. In fact so wrong you should hang your head in shame. You scored -100 points out of a possible +10. Cheated by using computer software and STILL got it wrong.

 

[gasbanni]

Haha, so much BS in this thread, yea yea you boast you can do it but actually you can't that's why you've not done it. Of course, you need a special drawing board to do it! How convenient!

What a small minded individual you are, Boasting ?

you measure others by your own little perspective.

I viewed it as a mental challenge on how it could be worked out and posted out of interest.

Don't bother replying you are not worth brain space you little sad troll.

Your on my ignore list your post aren't worth looking at .......good riddance
troll boy.

 

[gasbanni]

Been a bit busy but estimate is 950cm³ (volume of a cylinder removed of radius 1cm, length approximately √300 cm, being approx 50cm³) , will work out later. Got the method/shape in my head, doesn't need calculus; pythagoras is as hard as it gets.

If I get it wrong I shall remember to take Freddies lead and blame my tool, which in my case will be a pen and paper.

since when did pythagoras take into account arcs ?

of your funny shape.

My funny shape ? its the answer to the problem !

Ive definitively posted a way it can be done.

I await your answer with baited breadth intrigued as to how Pythagoras and using equilateral triangles can solve this problem and using a formula for calculating the volume of a cone. As none of these apply to this problem.

It would be like me quoting a wikipedia page on quadratic equations pointless !

 

[freddiemercurystwin]

You're not worth replying to that's why I sat down and put this crappy reply together, gonna ignore you you big bully

 

[gasbanni]

There are several right angled triangles involved if you want to get the answer.

Well Freddie your attempt was embarrasingly wrong. In fact so wrong you should hang your head in shame. You scored -100 points out of a possible +10. Cheated by using computer software and STILL got it wrong.

My Mistake ! just looked at my sketch there is one Right angle triangle !


However Pythagoras doesn't apply to the other three faces.

 

[freddiemercurystwin]

 

[chapeau]

Ive definitively posted a way it can be done.

You are on the right track but have missed one fundamental item....

It's in my explanation of how to do it.....



Pythagaros is everywhere.

 

[chapeau]

Reet no computer software for me, pen and paper. This diagram should help to explain better my written explanation above. So read the two in conjunction.

Untitled

• chapeau
• 18 Nov 2012
• 1

It's a 2D represation of a 3D problem but should show basics. All key unknown measurements on there. (plus what we know i.e. 10cm square allows it to be worked out using Pythagaros)

So far it's flummoxed 5 maths graduates, an MSc in maths and three science teachers with PhD's!

O-level question back in my day, though almost certainly a hard one. An A-level student back in my day should have been able to do it without much thought.