# How to adjust the required amounts of ingredients based on the diameter of the cake?

I have a question I have been asked to solve as part of my practice, however I am having some problems with figuring out the theory behind them.

Here are the important details

Ingredients for a 25cm diameter cake.

• 600g icing sugar
• 30g egg white

Question:

Roughly, what weight of each icing ingredient will he need? Explain how you arrived to your answer.

The cake sizes: 30cm, 25cm, 20cm.

As we already have 25cm I can cross that off.

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The title mentions integers but the body doesn't. Is "roughly" supposed to mean "rounded to the nearest integer"? –  joriki Feb 7 '13 at 13:36
I believe so, I think it means there is a little bit of leway on the answer –  Bradly Spicer Feb 7 '13 at 13:43

There's not enough information to answer the question since we don't know the dimensions of the various cakes. However, under the assumption that the lengths listed after "cake sizes" are meant to be interpreted as diameters and that the heights of the cakes are all meant to be the same, the volume of the cakes is proportional to the square of the diameter, so the weights of the ingredients need to be multiplied by the factors $(30/25)^2=1.44$ and $(20/25)^2=0.64$, respectively.