Math class

[Chicago Bob]

Is this the right way to convert? Thank you.

  7     X
12    10      7x10divided by 12...X= 5.8

So if I use 7oz dough in 12in pan     I need 5.8oz dough for 10in pan    right?

[SquirrelFlight]

If you're looking to maintain the same thickness, then you'll need to compare the ratio of weight to the area of the bottom of the pan. 

Area  = pi*r^2  (r is radius)

d = 2*r so Area = (pi/4)*d^2

So your proportions come out
7                      x
(pi/4)*144         (pi/4)*100

Noting that the pi/4's will cancel out:
7              x
144          100

So, x = 7*100/144 ~=  4.9

[Qarl]

Edit:  Darn...  Squirrel beat me to it!


Well, I think you really need to count for surface area (square inches of pan) and thickness

If thickness were equal... then you would just need to deal with suface area... = pi x radius squared


12" pan = 6" radius  Surface area = pi x radius x radius = 113.09 square inches
10" pan = 5" radius  Surface area = pi x radius x radius = 78.539 square inches

If 7 ounces spread over 113.09 square inches (12-inch pan), then ounces over 78.539 square inches (10-inch pan)

Yes, you would use the same fractions like you did

7/113.09 =  x/78.539

7x78.539 divided by 113.09 =  4.861 ounces...

[TXCraig1]

It doesn't need to be as difficult as either of those examples.

Since both pans are circles, pi drops off both sides and you get 7oz/36 = x/25

x = 7/36*25 = 4.861oz

[Chicago Bob]

Got it...thank you fellas.
I'm glad I mentioned a pizza pan. Guess the way I worked it would just be for straight line numbers....

[Pete-zza]

Bob,

The way I do it is 7 x 25/36 = 4.86 ounces. The math works the same when when you scale up. For example, for a 14" pizza, the math is 7 x 49/36 = 9.53 ounces. The same approach can also be used for sauce and cheese and toppings although that won't be quite as exact because the sauce and cheese and toppings stop short of the rim of the pizza, if the pizza has a rim. It is more accurate for a rimless pizza, like a cracker style.

Peter

[Chicago Bob]

It doesn't need to be as difficult as either of those examples.

Since both pans are circles, pi drops off both sides and you get 7oz/36 = x/25

x = 7/36*25 = 4.861oz

since both are circles you can just drop the r....correcto?

[Chicago Bob]

Bob,

The way I do it is 7 x 25/36 = 4.86 ounces. The math works the same when when you scale up. For example, for a 14" pizza, the math is 7 x 49/36 = 9.53 ounces. The same approach can also be used for sauce and cheese although that won't be quite as exact because the sauce and cheese stop short of the rim of the pizza, if the pizza has a rim. It is more accurate for a rimless pizza, like a cracker style.

Peter

Awesome...you guys are smart! Thank you

[Pete-zza]

since both are circles you can just drop the r....correcto?

It is Pi (3.14159) that drops out.

Peter

[Chicago Bob]

OK now    7/36    X/25      where did the 36 and the 25 come from the original   12    and   10

[Qarl]

25 is radius squared 5x5 for 10" pan
36 is radius squared 6x6 for 12" pan

[Chicago Bob]

25 is radius squared 5x5 for 10" pan
36 is radius squared 6x6 for 12" pan

Oh man...thank you. I forgot that part....r-squared. They were saying just drop the pi...now I get it. Literally, exactly ..drop only the pi part!  duh...

[SquirrelFlight]

Since everything here is a ratio, you don't even need to convert diameter to radius.  Just square the diameters to get the ratio.

Going from 10" to 12", the ratio is 144/100.

Going from 12" to 14", the ratio is 196/144


and so on.