SOLUTION: This is a gre math problem.... a certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Julie wants to use the recipe to make a cake of the

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Question 118675: This is a gre math problem....
a certain cake recipe states that the cake should be baked in a pan 8 inches in diameter. If Julie wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should she muiltiply the ingredients?
my answer: 1.5 but this is wrong and statistics show that over 65% of the people taking the test got this wrong answer...
The correct answer is 2.25...why???
If you can help, thanks!
Answer by Fombitz(32388) (Show Source):
You can put this solution on YOUR website!
Cake batter volume is the real variable that you're interested in here.
With a larger pan, you need more batter.
With a smaller pan, you need less batter.
For the same volume, you will have a definite relationship between the height and diamter.
The volume of the cake batter depends on the diameter of the pan and on the height of the pan.
For a cylindrical pan, the volume is

Originally let's use the subscript 1 to refer to 8 inch diameter pan.

When it's a 12 inch diameter pan let's use subscript 2.

Now let's plug in some numbers.

And for pan 2,

Also, remember the depth is the same.

1.
2.
of re-writing the equation 2.

Now plug that value back into equation 1.
1.

So you need 2.25 times as much batter, so you multply all of the batter ingredients by 2.25.