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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