Time it takes for a cake to cool

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Hey baking fans,

I am new to baking and when I first started I had difficulty icing the cake rushing it and the icing would melt. For school I was given the opportunity to mathematically find the right temperature can be frosted at with out it melting. Now my frosting had milk, butter, thickened cream and icing sugar, and maybe if your ingredients are different time will be different, but let me know and I can get back to you with the right time. So, my cake was in a round 8.5 inch wide pan with a height of 2.5 inches, and I poured 3 and 2/3 cups of batter in and baked it at 150 fan forced for 52 minutes and it will take 3 hours 26 minutes and 40 seconds before you can frost it, and I have tried it and your icing won't melt. I also came up with a rule that for every extra metric cup of batter, you add from 3 2/3 cups, it is an extra 120 minutes and 40 seconds in a pan which is 8.5 inches wide. Hope I can help and let me know if I can do anything. Marcus
 

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