Math is Real Life: Tart Time

It’s the first Wednesday of October, and I am joining some other great teachers out there for the Math IS Real Life!! link up hosted by Miss Math Dork.  The idea is that we show how we use math in our real lives.

As my regular readers know, I love to cook and aspire to be a chef (well, really only in my own kitchen, I would never survive restaurant hours.  Anyway, this past week we were having friends over, and I made two tarts: a lemon tart and a dark chocolate raspberry tart.  
The dark chocolate tart called for a 9" tart pan, but I wanted to use a 5 1/2" tart pan.  In order to figure out how much crust and filling I needed, I had to reduce the recipe.  Now, just looking at the recipe one might think that I would need about 2/3 of both the filling and the tart, but unfortunately, it simply wasn't that simple. 

mathisreallife-revisedI needed to calculate the surface area (for the crust) and actual volume (for the filling) of each pan and their ratios in order to change the ratios in the recipe.  The surface area of the bigger pan is 155.1 inches.  The surface area of the smaller pan is 64.8 inches.  I needed 64.8/155 of my tart which calculates to approximately .44 of the recipe, or a little less than half.  
For the volume:
the 9" tart pan volume = 63.62 inches squared
the 5.5" tart pan volume = 23.76 inches squared
23.76/63.62 = .38  So, really I needed only a little more than 1/3 of the filling and with the raspberries not changing in size, I calculated the volume of the filling to be 1/3 of the original recipe.  This worked great, and I had very little filling (or tart) left over.

Check out other great ideas for math in real-life with the link from Miss Math Dork.