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

[noonar]

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]

ps would you also need to know the 'intended' depth of cheesecake??

[TheSkiingGardener]

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

22 squared divided by 20 squared?

[TheChewyToffeeMum]

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]

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

[MrsSnaplegs]

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 need
What depth is your tin?

[HauntedLittleLunatic]

25% is correct answer to keep same depth.

[HauntedLittleLunatic]

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]

I think 21% too


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

so ratio is 1.21

[RustyBear]

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]

1.21:1 sorry

[HauntedLittleLunatic]

Sorry rusty....areas are 1257 cm2 and 1521cm2 which is 21% increase.

[RustyBear]

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]

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

[noonar]

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

some very scary maths boffs on here

[noonar]

ah another mistake "10%" is what i thought

[MmeBlueberry]

21%

[GreenTeapot]

Only on Mumsnet ...

[RustyBear]

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%

[RustyBear]

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

[HauntedLittleLunatic]

Oh yes I have used diameter not radius



But you are right % increase the same!

[StealthPolarBear]

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

[RustyBear]

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

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]

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 :))

[RustyBear]

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'

[StealthPolarBear]

Sorry to put a downer on this thread but my Grandma died earlier this week and you remind me of when I used to "help" her make scones when I was a child. She didn't use scales so I'd tip out the flour and she'd say stop when she judged, by eye, that there was enough. She was never wrong.