I have drilled a hole.........

AncientMariner over 3 years ago

Well, I did not drill it, but about 50 years ago a colleague produced this question from his book:

"A cylindrical hole six inches long has been drilled straight through the centre of a solid sphere. What is the volume remaining in the sphere?"

Enjoy!

Clive

0 Chris Pearson over 3 years ago

Simon Barker:

I'm not sure what it means for a hole to have domed ends. What's the shape of something that isn't there?

What a fascinating question and solution!

My mistake was to think of the core which has been removed, but evidently, the drill would have to have a cutting capacity longer than 6".

Concerning Mike's point about Oxford and Cambridge entry, I think that they barely relied at all on A-levels in my day. After all, with 4th term entry, A-levels were two terms away.
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0 mapj1 over 3 years ago

There’s a Saturday night challenge, work out the area of a circle by using a quarter of the circumference squared rather than by A = π r² and compare the results.

Circumference =2 π r

Quarter Circumference =π r/2

square of Quarter circumference = r² π² /4 =r² * 2,468 approx

Area of circle total = π r² =r² * 3,14 approx

Suggests you lose about a quarter of the volume in the process of making it into rectangular planks. which feels quite good to me,
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0 Sparkingchip over 3 years ago

But remember any "waste" can be sold as firewood, so is not really waste.
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