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really hard grown up MATHS problem involving volume...help!

(29 Posts)
noonar Sat 09-Jul-11 07:55:28

I am making a chessescake, but have only a 22cm circular cake tin, instead of the required 20cm tin. By what percentage do I need to increase the ingredients? As DH has already pointed out, my initial response of 20% is incorrect! can anyone help??

noonar Sat 09-Jul-11 07:57:31

ps would you also need to know the 'intended' depth of cheesecake?? hmm
<too clever for me emoticon>

TheSkiingGardener Sat 09-Jul-11 08:01:02

Why is 20% incorrect? That's what I make it.

22 squared divided by 20 squared?

TheChewyToffeeMum Sat 09-Jul-11 08:01:28

Hi

To go from 8" (20cm) to 9" (23cm) you need to add 1/4 ie 125%. Is your tin definitely 22cm? If it is then 20% is probably not far off.

PatientGriselda Sat 09-Jul-11 08:02:01

Not exactly answering the question, but from a practical point of view, why not just make a shallower cheesecake?

MrsSnaplegs Sat 09-Jul-11 08:02:32

I would say 10%
2cm is 10% of 20cm and that is what you have increased surface area by but thinking about it that's probably wrong as it's volume you needsad
What depth is your tin?

HauntedLittleLunatic Sat 09-Jul-11 08:03:43

25% is correct answer to keep same depth.

HauntedLittleLunatic Sat 09-Jul-11 08:09:38

Actually just calculated with calculator and 21% is actually correct.

Multiplying everything by 20 or 25% though will be fine -whichever is easiest from your numbers.

StealthPolarBear Sat 09-Jul-11 08:16:19

I think 21% too

surface area of bigger one is 121pi
smaller one 100pi

so ratio is 1.21

RustyBear Sat 09-Jul-11 08:16:41

20cm tin is approx 314cm in area, 22cm approx 380, which is 25% more. If you want the same depth of cheesecake that's all you need to increase it by.

StealthPolarBear Sat 09-Jul-11 08:16:42

1.21:1 sorry

HauntedLittleLunatic Sat 09-Jul-11 08:23:00

Sorry rusty....areas are 1257 cm^2 and 1521cm^2 which is 21% increase.

RustyBear Sat 09-Jul-11 08:25:50

Sorry meant to say 'between 20 & 25% more', the difference is 66 cm, which is 1/4.75 of 314.

If you're going to turn the cheesecake out to serve it, it might look better if you increased the depth too, which is why I suggested 25% - if there's any mixture left over, you can always eat it yourself...

HauntedLittleLunatic Sat 09-Jul-11 08:28:57

That's true actualy if it is bigger in area maybe it would look aesthetically better if it is also a little deeper.

noonar Sat 09-Jul-11 08:32:29

wow, thanks folks. i made a mistake in my original post: i thought it would be 105 like mrs snap. that was def wrong. will increase by 25% and them will ahve enough for ramikins for the dcs too!

its a for a dinner party, and i dont wnat to end up with a pancake, pateient grin

some very scary maths boffs on here grin

noonar Sat 09-Jul-11 08:33:13

ah another mistake "10%" is what i thought

MmeBlueberry Sat 09-Jul-11 08:45:01

21%

GreenTeapot Sat 09-Jul-11 08:50:23

Only on Mumsnet ... grin

RustyBear Sat 09-Jul-11 08:54:38

Haunted - are you sure about those areas? 1257^2cm is pretty big.....

Area = pi (r^2) =(approx) 3.14x (10x10) = 3.14x100= 314
You seem to have done 4 pi r^2, which is the surface area of a sphere.

Though in fact in terms of percentage difference, it works out the same, and your 21% was actually closer than my 25%

<I am rapidly finding out where all the punctuation is on my iPad keyboard!>

RustyBear Sat 09-Jul-11 08:58:28

actually, I just keep thinking 'Pie are not square. Pie are round.....' grin

HauntedLittleLunatic Sat 09-Jul-11 09:01:50

Oh yes I have used diameter not radius <doh>

<hangs head in shame>

But you are right % increase the same!

StealthPolarBear Sat 09-Jul-11 09:10:45

Rusty - is 21% not exactly correct? You can ignore the pi, it cancels out, surely

RustyBear Sat 09-Jul-11 09:27:31

Yes, it is, exactly correct is 'closer' than not correct, isn't it! grin

Tbh, I'm not used to exact calculations when I'm cooking, I tend to measure/weigh roughly & chuck a bit more in if I think it needs it; it all comes out pretty good, so I must be doing it fairly accurately!

StealthPolarBear Sat 09-Jul-11 09:45:22

ah sorry was just checking because I wanted to know if I was wrong
I agree though - in the context of cooking 21% and 25% isn't going to make much difference
(I am a dreadful cook though smile)

RustyBear Sat 09-Jul-11 10:02:05

My method does make it a bit difficult when it comes to teaching DC how to cook though - "just add milk until it's not too stiff" isn't too helpful.

And I completely threw DD with my explanation of when peas are cooked, as 'when it feels right when you stir them with a wooden spoon'

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