betsy wrote:
> Dave Bell wrote:
>
>>in her garden wrote:
>>
>>
>>>First post to this newsgroup. I want a nice, generic butter cake
>>>recipe that will fit into a 10" springform pan. 10" seems to be a nice
>>>size to serve 8. I usually serve this type of cake plain or topped
>>>with whipped cream, ice cream or fruit.
>>>
>>>If you either have a ready-sized recipe or you can tell me how to
>>>retool my (two 8" cake pans) recipe, that would be great. Or perhaps
>>>you know a website that discusses this?
>>
>>Well, the 10" pan relative to an 8" pan is 56% bigger.
>>(10*10/8*8 = 100/64 = 1.5625)
>>If it is also 25% deeper, that's almost exactly twice the volume. (1.95)
>>I would use the 2-8" recipe as-is, for size.
>>
>>
>>>If I were to use my (two 8" cake pans) recipe, I suspect I'd need to
>>>lengthen the baking time for my recipe, but would I need to lower/raise
>>>the baking temperature, too?
>>
>>Yes, I would lower the temp a little, say from 350F to 325F, and bake
>>somewhat longer. Start checking about every 10 minutes past the original
>>time, until a toothpick comes out clean...
>>
>>Dave
>
>
> Well, um, er forgive me for butting in, but your formula above is for
> square pans. To get the surface area of a round pan, the formula is pi
> * r-squared. I can't write "pi" or a superscript for "squared". So, a
> 10" pan, 10 is the diameter, 5 is the radius, 5 squared is 25, times pi
> (3.14) = 78.6 square inches
>
> The 8" pan is 50.2 square inches (pi * 16, 4 being the radius)
>
> The 8" is 64% of the 10 inch, not allowing for height. To get volume,
> multiply the square inches of the pan by the height. So if the 8" pan
> gets a 1.5" high cake, then it would have a volume of approximately
> 75 cubic inches. That's roughly equal to a 1" height in the 10" pan.
> If you make the equivalent of 2 8" cake recipes, then a 10" pan would
> have a cake height of not quite 2 inches, which would look "right" for
> that size.

Ahem.... Note that I was comparing areas and volumes as *ratios*,
therrefore Pi was irrelevant. As did you, when you said the 8" pan was
64% of the 10", except I said the 10" was 156% of the 8". (OK, 156.25%,
so sue me!) I then multiplied by the 125% in height, and voila - 1.95X.

> Anyway, better living through chemistry and geometry, _this_ is why you
> need math in school!
> Cheers,
> betsy (an engineer, could you guess that?)

Yep, and so am I...

Dave

(Worst example I ever saw in public of extra effort like above was in a
pond magazine. They took about a 4"x6" box to explain how to calculate a
10% water change: Assume a rectangular pond, with straight sides.
Multiply the lenght times to width to get the area in square feet. The
multiply the area by the depth (in inches), then divide by 12 to get
volume in cubic feet. Multiply that by 7.45 to get gallons. Take 10% of
that volume. Divide that by the area (from above) to get the change in
depth (in feet), and finally, multiply that by 12, to get inches! All
accompanied by a worked example of something like a 10' by 15' pond, 30
inches deep.

"Or", I said, "take 10% of the depth in inches. 30 * 1/10 = 3 inches")