Carcass 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) \(2 \frac{1}{2}\)

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

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

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

(E) \(1 \frac{1}{3}\)

The main idea here is that the volume of ingredients needed is proportional to the volume of the cake. For example,

if the volume of the cake with diameter 12 is TWICE the volume of the cake with diameter 8, then we will need TWICE has many ingredients.

Although the question doesn't mention it, the shape of the cake is cylindrical.

Volume of cylinder \(= \pi r^2 h\)ORIGINAL CAKEOriginal cake recipe requires a pan with an 8-inch diameter.

If the diameter is 8 inches, then the RADIUS = 4 inches

Since we don't know the height of the cake, let's just use the variable \(h\) to represent the height

So, the volume \(= \pi (4^2)h\)

Simplify to get: \(= 16\pi h\)

DIFFERENT CAKEThis cake requires a pan with an 12-inch diameter, which means the RADIUS = 6 inches

So, the volume \(= \pi (6^2)h\)

Simplify to get: \(= 36\pi h\)

The question becomes, "\(= 36\pi h\) is how many times greater than \(= 16\pi h\)?"

To answer this, we must simplify: \(\frac{36\pi h}{16\pi h}\)

Cancel \(pi h\) to get: \(\frac{36}{16}\)

Simplify further to get: \(\frac{9}{4}\)

Rewrite as mixed fraction: \(2\frac{1}{4}\)

Answer: B

Cheers,

Brent

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Brent Hanneson – Creator of greenlighttestprep.com

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