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# A certain cake recipe states that the cake should be baked

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Eternal Intern
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A certain cake recipe states that the cake should be baked [#permalink]

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22 Jul 2003, 08:58
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A certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Jules wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should he multiply the recipe ingredients?
Manager
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22 Jul 2003, 09:53
First, know that this is a circular pan with a certain height (...so cylindrical i guess...)

Just compare the ratio of the volumes of the two cakes, we will call the desired height H.

Remember pi * r^2 * H is the volume

First: 16 pi * H

Second: 36 pi * H

The instructions calculate the ingredients based on the first pan measurement, so you must multiply them by 36/16 (answer prob reduces this to 9/4) for them to work for the second.
Eternal Intern
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22 Jul 2003, 10:38
What do they mean by the "same Depth"?

How do we know height is constant?
Manager
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22 Jul 2003, 10:45
To me, "same depth" implies that height is constant. If you stick your finger in the 8 inch cake it will go as far in as if you did the 12 in. cake. - that is depth, and in this case when you model the cylinder, it is height.
SVP
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22 Jul 2003, 11:33
V1/V2=pi*12^2*height/pi*8^2*height=12*12/8*8=9/4
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