short maths question

[shirt]

my mum has a nintendo DS and has annoyed me for most of christmas by playing 'professor layton & pandora's box' and asking me questions every 2 minutes when she can't work out a puzzle.

its been easy, but one she asked me earlier was particularly annoying as i know i'm right.

with reference to this pic:



in short, if each circle has a radius of 10m. what is the area of the shaded area to the nearest metre squared?

this isn't difficult in my eyes: (20^2) - (Pi x 10^2) = 400 - 314 = 86m sq.

nintendo reckons the answer is 400m sq. even the diagram to show their working makes this answer look stupid, so am i wrong or is nintendo on a mission to confuse old people?

[wendyg]

400m/2 is clearly wrong, and the correct answer will arrive eventually (from some one else)

[BarnatosGhost]

shirt, either you're right, or you're just as wrong as i am.

[wendyg]

I'm thinking 86m/sq


Only just noticed that you posted that before

Edited by wendyg on Monday 28th December 22:32

[mrmr96]

Well it's not 400m2. You could draw a square by connecting the centre point of each circle. This would have 4 sides of 20m each, total being 400m2. The shaded area fits inside this box and is clearly smaller than the box, so it must be less than 400m2. So Nintendo is wrong.

Don't immediately see how to calc the area, but I'll get back to you, unless someone beats me to it!

[Alan Alan Alan]

I think this is the Nintendo way

http://www.algebra.com/algebra/homework/Surface-ar...

[shirt]

mrmr96 said:

Well it's not 400m2. You could draw a square by connecting the centre point of each circle. This would have 4 sides of 20m each, total being 400m2. The shaded area fits inside this box and is clearly smaller than the box, so it must be less than 400m2.

this is how nintendo say its done

mrmr96 said:

So Nintendo is wrong.

i reckon so. my poor old mum!

[mrmr96]

Ok, I've just checked your workings and I agree. Start off with the square I described, which links the centre of each square, this gives 20 x 20 = 400m2 square. Then you need to take out the bits where the circles are, so 4 lots of a quarter of a circle. So 4 x (1/4) x Pi x 10^2 (as r=10).

So yeah, 86m2.

[StuWS]

I get 86 as well.

Draw a square from the centre of each circle through the circles tangent points.

Doing this disects each circle into 4.

Square area = 400m^2

Less 1/4 * area of a circle * 4 = 314

400 - 314 = 86m^2

Edited by StuWS on Monday 28th December 22:30

[Roger645]

If you read this:

http://professorlayton2walkthrough.blogspot.com/20...

It also includes one flowerbed as well as the centre bit

[StuWS]

Roger645 said:

If you read this:

http://professorlayton2walkthrough.blogspot.com/20...

It also includes one flowerbed as well as the centre bit

[mrmr96]

The OP got the right answer but for the wrong question!
Ah well, at least your maths isn't at fault, just your interpretation of the diagram in the game.

[shirt]

Roger645 said:

If you read this:

http://professorlayton2walkthrough.blogspot.com/20...

It also includes one flowerbed as well as the centre bit

ah, didn't realise it included the circle as well, i was shown it on a bit of paper.

on the plus side, it seems my mum loves discovery quest - especially x-machines and american hotrod!

[Hoady]

I spent ages on this one too - the pic on the DS does appear to show the centre bit only and I kicked myself when I realised it included one of the circles as it suddenly became so easy...

[CaptainSlow]

see here???

http://www.pistonheads.com/gassing/topic.asp?h=0&a...