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

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A certain cake recipe states that the cake should be baked i [#permalink]  22 Mar 2018, 03:13
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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?

(A) $$2 \frac{1}{2}$$

(B) $$2 \frac{1}{4}$$

(C) $$1 \frac{1}{2}$$

(D) $$1 \frac{4}{9}$$

(E) $$1 \frac{1}{3}$$
[Reveal] Spoiler: OA

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Re: A certain cake recipe states that the cake should be baked i [#permalink]  22 Mar 2018, 20:16
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One way to solve this problem is to find the actual areas of the 8 inch diameter pie, and the area of the 12 inch diameter pie, and divide the latter by the former. But this problem can be solved almost instantly if you know a very useful rule: if you multiply any length of one shape to get the length of a similar shape, then if you want the area of the latter shape, you can simply square the multiplier you just used. Here's a simple example. If you have two similar triangles, and the perimeter of the larger triangle is 3 times that of the smaller triangle, then you know the area is 3^2 times larger, or 9 times larger.

So, using this technique, when we see that the ratio of pie diameter is 12 to 8, or 3/2, we can simply square 3/2, getting 9/4, which is B.
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Re: A certain cake recipe states that the cake should be baked i   [#permalink] 22 Mar 2018, 20:16
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