I’m 70, so no, this isn’t homework. I’m usually pretty good at this stuff, but this has me stumped. I’m planning to make mince tarts this week, which requires pie dough cut into small circles, say about 3" in diameter. Rather than guess how many pie crusts I need to buy, I’d like to be able to come up with an estimate.
So the question is, how many 3" circles can I get from a 9" pie crust? If someone can provide a formula for figuring this out, I’d appreciate it.
I would guess nine, three rows of three.
Wait the pie crust is round.
NM
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You’ll be able to get three across at the center. You’ll be able to get three down at the center. That makes five, and I’m not thinking there’s any more efficient use of the space, since any way you rotate it will lead to a similar pattern.
You could instead get two across as soon as there’s an arc with a length of 6 inches, but I think that’d lead to a total of four, not five.
My apologies if I’m missing something obvious :).
That’s what I came up with more slowly than you using geometry rather than algebra. 
Can the remaining dough be remixed and used?
(Radius of larger)[sup]2[/sup] ÷ (radius of smaller)[sup]2[/sup] = number of smaller that can be made from larger … both factors have a π term but I’ve taken the liberty to cancel those out for you …
The answer to the example is 9[sup]2[/sup] ÷ 3[sup]2[/sup] = 9 …
That’s what I wondered.
The amount of dough in a 9" diameter (4.5" radius) circular pie crust (pi * 4.5²) is 9 times as much as the amount of dough in a 3" pie crust (pi * 1.5²).
On preview, I see that watchwolf49 has already calculated this. He used diameters instead of radii in his calculation, but it doesn’t matter if all you care about is the ratio.
If you roll out the remaining scraps then you can make 9[sup]2[/sup] / 3[sup]2[/sup] = 9, of course. (The pis cancel out; hopefully the pies won’t.)
Edit: beaten to it.
Nine, not nine recurring 
[hangs head in shame] … my only excuse is that I always use diameter when filling out tax forms …
This is really embarrassing, but then it’s only just 6 a.m. and I’ve been up for two hours without coffee. The above seems logical. But what if I started at the top and then worked around the perimeter with the small circles touching each other? Do I gain anything, or do I end up the same?
If you can salvage the scraps and roll them out again to the original thickness, you can get exactly 9 tarts from one pie crust (nine squared divided by three squared). If the scraps are waste and can’t be reused, you can get 7 three-inch circles from one nine-inch crust. (cite)
If you don’t want to use the scraps - 7
Get 7 coins of the same denomination and circle 6 of them around the seventh for a good visual.
I think you end up the same. That way you can fit 5 circles around the perimeter but there’s not enough dough in the center for another pie.
According to this website for a nine inch pie crust, you can get 14 with a 2" diameter, 8 with a 2.5", 5 with a 3", 4 with a 3.5" and 3 with a 4".
You can pack 7 circles of radius 3 into a circle of radius 9, but no more.
No, you can fit one 3" circle exactly in the centre and another six all the way round, touching each other.
Like so: Imgur: The magic of the Internet
Then if you take the leftover pieces and re-roll to the same thickness you should have exactly enough for two more.
Great! And yes, I can re-roll the scraps.
It just occurred to me that we should have asked what you meant when you said a nine-inch crust. Is it a crust with a known diameter of nine inches or a crust designed to fit in a 9-inch pie pan? If the latter, it will have to be bigger than 9 inches in diameter, in order to fit up the sides with some left over for edges. The ones I’ve bought in the past were probably at least 12 inches in diameter, maybe 13 or a little more. Assuming 12 inches you should be able to get 16 three-inch circles if you reuse the scraps.
Wouldn’t it be easier to just buy the little tart shells?
Hey!
That’s cheating!
:smack:
Double :smack:
