Bunuel wrote:
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?
(A) 2 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3
We need the volumes of the two cake pans. Either: just calculate difference in area because only two of the three lengths change; or assign a value for height (depth of the pan) and run the numbers.
You can calculate for square or a round pan. I chose square.
Area onlyA square cake pan with an 8-inch diagonal will have sides that = \(\frac{8}{\sqrt{2}}\) inches
Area = \(\frac{8}{\sqrt{2}} * \frac{8}{\sqrt{2}} =(\frac{64}{2})=32\) square inches
Sides of cake pan with 12-inch diagonal have length:\(\frac{12}{\sqrt{2}}\) inches
Area of cake pan with 12-inch diagonal:
\(\frac{12}{\sqrt{2}}* \frac{12}{\sqrt{2}}=(\frac{144}{2})=72\) square inches
The increase factor of both cake pan volume and recipe:\(\frac{72}{32}=\frac{9}{4}=\)
\(2\frac{1}{4}\)
Answer B
Volume Pick a depth (height) - it does not change, so it does not matter what you pick.
First pan is 8 inches in diameter. Let height = 2 inches
The sides of the pan, in length = \(\frac{8}{\sqrt{2}}\) inches
Volume of original pan, L*H*W, is \(\frac{8}{\sqrt{2}} *\frac{8}{\sqrt{2}} * 2= (\frac{64*2}{2})=64\) cubic inches
When the pan's diameter is 12 inches, its sides =\(\frac{12}{\sqrt{2}}\) inches
Height = 2 inches
Volume of 12-inch diameter pan is L*H*W:
\(\frac{12}{\sqrt{2}} * \frac{12}{\sqrt{2}} * 2 = (\frac{12*2}{2})=144\) cubic inches
By what factor has volume increased (= factor by which recipe must be increased)?
\(\frac{144}{64}=\frac{18}{8}=\frac{9}{2}=\)
\(2\frac{1}{4}\)
Answer B
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