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sweet tooth
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PostPosted: Thu Sep 08, 2011 8:41 pm    Post subject: Pans Reply with quote

question does two 8 inch by 2 inch rounds bake faster than a 13x9x2 pan. I would think they would bec. of more surface area with the rounds. but according to a site i went to this isnt so. So I am not sure what to bel. now.The site i went is ..well first go to google and then type in There's more to baking time than pan size... by online Athens.

thanks ahead of time.
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Dilbert



Joined: 19 Oct 2007
Posts: 971
Location: central PA

PostPosted: Thu Sep 08, 2011 10:35 pm    Post subject: Reply with quote

the article explains the situation quite clearly.

the amount of batter in two 8 inch round pans will not fill a 13x9 to the same depth - the 13x9 has more surface area.
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sweet tooth
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PostPosted: Fri Sep 09, 2011 2:41 am    Post subject: Pans Reply with quote

yes i know it explains it. my question is 2 rounds cook faster than a 13x9x2,is what everyone tells me and on a cake box it says same thing. dont know what to go by? according to web site the 13x9x2 cooks faster,bPut everyone else says small bakes faster than a big pan
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brown sugar
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PostPosted: Sat Sep 10, 2011 3:10 am    Post subject: pans Reply with quote

sweet tooth...I have always wanted to know something close to your question but I worded this way... when u read things on cooking or baking they talk about the surface area a lot and they say if the surface area is bigger, less bake time and if smaller area, more bake time and with the two 8inch rounds they are saying less bake time, bec. pan is smaller. But if go by surface area being less would be more bake time. Also read bigger pan more bake time bec. takes time to heat pan up. So I would like some one here to kindly explain this? How can it be both ways? More bake time for less surface area,but if smaller pan faster bake time?(smaller pan less surface area).
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Michael Chu



Joined: 10 May 2005
Posts: 1606
Location: Austin, TX (USA)

PostPosted: Sat Sep 10, 2011 7:11 am    Post subject: Reply with quote

2 8-in baking pans should take more time to bake than the same volume of batter in a single 9x13 pan. In general, (1) the more surface area there is on the top, the faster it will bake, (2) the more TOTAL surface area there is the faster it will bake, and (3) the shallower the batter, the faster it will bake. Let's examine this case:

2 8-in baking pans filled two inches deep:
surface area of a single pan: approx 50 sq in ( (8/2)^2*pi )
depth of batter in each pan: 2 in
total surface area (making contact with batter) of a single pan: approx 150 sq in ( (8/2)^2*pi+(8/2)^2*pi+8*pi*2 )
surface area of both pans: ~100 sq in
total surface area of both pans: ~300 sq in

compared to
1 9x13 baking pan (assuming it is a cuboid shape for simplicity):
surface area of pan: 117 sq in (9x13)
depth of batter in pan: ~1.7 in (200 cubic in of batter / 117 sq in)
total surface area of pan (making contact with batter): ~309 sq in (9x13+9x13+1.7*(9+9+13+13))

The surface area of the 9x13 is larger than 2 8-in rounds and depth is less in the 9x13, so all signs point to the 9x13 taking less time to bake the same amount of batter when compared to two 8-in rounds.

However, the difference in material of the pans and how long it takes to heat up can be a large factor. Even though the 9x13 spreads the batter out more and is shallower in depth and everything points to it cooking faster, if the material takes a long time to heat up (like really thick metal used in the 9x13 pan vs thin metal in the rounds) it could conceivably take longer to bake. If the materials are the same, then in all likelihood the 9x13 pan will bake faster.


Last edited by Michael Chu on Mon Sep 12, 2011 8:02 pm; edited 3 times in total
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sweet tooth
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PostPosted: Sun Sep 11, 2011 2:36 am    Post subject: Pans Reply with quote

could u explain why for total surface area on the 8 rounds u do it 3 times,and on the 13x9 all the pans i seen are 2 inch deep .

thank you
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sweet tooth
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PostPosted: Sun Sep 11, 2011 2:48 am    Post subject: Pans Reply with quote

also, can u explain why they say big pans take longer to bake than smaller pans.Bec. by what u said this isnt true. Asking bec. just started baking and like to understand.
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brown sugar
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PostPosted: Sun Sep 11, 2011 2:55 am    Post subject: Pans Reply with quote

Hey,
For a beginner thats a lot to take in! Any other way thats simple than doing all that?
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r2d2
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PostPosted: Mon Sep 12, 2011 3:00 pm    Post subject: Pans Reply with quote

Chu,
Is your numbers right on the 13 x9 pan? I did the way u list it and I dont get 309. I took 117+117=234+1.7=235.7x44(9+9+13+13)do not get 309.Could u help on this.
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r2d2
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PostPosted: Mon Sep 12, 2011 3:25 pm    Post subject: Pans Reply with quote

Forgot to ask would this way be ok too for trying to figure out total surface area on 13x9x2....... 2x lxw +2x lxh +1x wxh.
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r2d2
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PostPosted: Mon Sep 12, 2011 3:42 pm    Post subject: Pans Reply with quote

Chhu,


Sorry on the last form. the one if i can use this to figure out total surface area. I copied it wrong suppose to be.....2x lxh +2x wxh +1x lxw... again will this work too on 13x9x2 pan with the same results.....saying 13x9 will cook faster. I know u are a busy person,but would appr. if u could help with my questions.
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Michael Chu



Joined: 10 May 2005
Posts: 1606
Location: Austin, TX (USA)

PostPosted: Mon Sep 12, 2011 8:07 pm    Post subject: Re: Pans Reply with quote

sweet tooth wrote:
could u explain why for total surface area on the 8 rounds u do it 3 times,and on the 13x9 all the pans i seen are 2 inch deep .

The first two are the top and bottom surface (each is 8/2^2*pi = 4^2*pi = 16*pi = ~50) and the third is the surface area of the side of the pan (circumference of pan * depth of batter = 8*pi*2).

For the 13x9 pan, the reason we don't use 2-in is because even though that is how deep the pan is, the batter does not go up that high. The portion of the pan above the batter does not conduct heat into the batter, so we leave it out of the equation. (Of course it has some effect on the cooking time, but it's small compared to the effect of the portion of the pan actually touching the batter. Since it is small, we leave that part out.) Since we know the volume of the batter, we can calculate how deep it is in the pan which is about 1.7-in.

sweet tooth wrote:
also, can u explain why they say big pans take longer to bake than smaller pans.Bec. by what u said this isnt true. Asking bec. just started baking and like to understand.

I think you misread the article. The article states "But what if the batter usually fits well in two 8-inch cake pans, another common size? In a 13-inch pan, the batter wouldn't be as deep and the baking time wouldn't be as long." Seems pretty clear they are saying the bigger pan takes less time to bake.

r2d2 wrote:
Is your numbers right on the 13 x9 pan? I did the way u list it and I dont get 309. I took 117+117=234+1.7=235.7x44(9+9+13+13)do not get 309.Could u help on this.

Check your order of operations.
9x13+9x13+1.7*(9+9+13+13) =
117 + 117 + 1.7*(44) =
234 + 74.8 =
308.8

r2d2 wrote:
Sorry on the last form. the one if i can use this to figure out total surface area. I copied it wrong suppose to be.....2x lxh +2x wxh +1x lxw... again will this work too on 13x9x2 pan with the same results.....saying 13x9 will cook faster. I know u are a busy person,but would appr. if u could help with my questions.

Yes, except the final term should be 2x lxw instead of 1x (the surface at the bottom of the pan counts too for total surface area of the batter in a 9x13 pan).
note that 2lh+2wh == h(2l+2w) == h(l+l+w+w) which is how I wrote it initially (sorry if that confused anyone).
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Michael Chu



Joined: 10 May 2005
Posts: 1606
Location: Austin, TX (USA)

PostPosted: Mon Sep 12, 2011 8:22 pm    Post subject: Re: Pans Reply with quote

brown sugar wrote:
Hey,
For a beginner thats a lot to take in! Any other way thats simple than doing all that?

Yeah, that's more math than anyone should need to do to figure out if something is going to cook longer or shorter. Assuming everyone has uniform pans (same size up and down), just calculate the surface areas of the two possibilities you are examining:
2 8-in cake rounds:
surface area = pi*(radius squared) (don't forget to times two because you have two cakes)

9x13 pan:
surface area = width * depth

compare the two numbers. Which ever one is larger should cook in less time. If they are the same, then assume it will cook in about the same amount of time.

These are just ballpark estimates - The first time you bake from any recipe, you should always check on the thing you are baking early in case your oven runs hotter than the oven the recipe writer used, in case your batter started at a warmer temperature, in case your pans are darker (this is actually a huge variable - a dark pan can cook 20-33% faster in some cases!), etc.
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r2d2
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PostPosted: Mon Sep 12, 2011 8:53 pm    Post subject: Pans Reply with quote

Chu

Hey thank you for the help.. But I do have two questions i would like u to answer too... and i promise no more. The 13x9 on your last answer says u do wxdepth... I know u are right but thought u do lxw for surface area? Also when i do the calc. for a 8x8x2 and a 9x2 round my calc. comes up for square 192 and when i do round comes up to 183 that is based of the round pie cala. dir. and the square is off of 2(lw+wh+hi).Based on that it tells me the 9...183 needs more cook time? Does this seem right? Sorry new to this and wanting to understand.
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Michael Chu



Joined: 10 May 2005
Posts: 1606
Location: Austin, TX (USA)

PostPosted: Mon Sep 12, 2011 9:51 pm    Post subject: Re: Pans Reply with quote

r2d2 wrote:
Hey thank you for the help.. But I do have two questions i would like u to answer too... and i promise no more. The 13x9 on your last answer says u do wxdepth... I know u are right but thought u do lxw for surface area?

Sorry, you are right - I meant to write length * width but messed up.

r2d2 wrote:
Also when i do the calc. for a 8x8x2 and a 9x2 round my calc. comes up for square 192 and when i do round comes up to 183 that is based of the round pie cala. dir. and the square is off of 2(lw+wh+hi).Based on that it tells me the 9...183 needs more cook time? Does this seem right? Sorry new to this and wanting to understand.

I'm glad you brought this example up. This is one of those examples where looking at top surface area alone does not necessarily give you an accurate prediction as to which will bake faster.
Looking at top surface area alone:
8x8 pan - top surface: 8x8 = 64 sq in.
9-in round - top surface: (9/2)^2*pi = 63.6 sq in.
This would indicate that it would take the same amount of time to bake

Looking at depth of batter:
8x8 pan: 2 in batter depth (as defined by the problem)
9-in round: the same amount of batter (128 cu in) would produce a depth of about 2 in as well
This would also indicate that it would take the same amount of time to bake

Looking at TOTAL surface area:
8x8 pan - total surface area: top+bottom+sides = 64+64+(2*8*4) = 192 sq in
9-in round: top+bottom+sides = 64+64+(9*pi*2) = 184.5
There is a little less (4%) surface area in the round pan than the square pan. This suggests that it would take longer to bake the batter in the round pan.

However, because the other calculations indicate same cooking time and the last calculation indicates a slight chance of longer cooking time, we're unable to say for sure what will happen in this case. All signs point to the baking times being very similar though (since even the total surface area difference was only a 4% difference). In this case, the other existing variables (thickness of pans, color of pans, material of pans, position in oven, hot spots in oven, etc) greatly outweigh any difference these two pans have with respect to baking times. I would not be surprised if they cook in the same amount of time or if EITHER pan took longer to bake.
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