cake recipe

gmattesttaker2 wrote:Hello,

Can you please tell me how to solve the following:

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

OA: B

Thanks,
Sri

Sri,
Actual Radius is 4
Final radius is 6

you have to compare by the square of the radius

4^2 and 6^2
16 and 36

so, 16*9/4 =36
Hence answer is B

Regards,
Uva.

gmattesttaker2 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?

Jules must necessarily be baking the cake in a Cylindrical container ( having some height at least )

Given the Original Diameter is 8 Inches , hence radius will be 4 inches

Let the depth of the Container be D

So , volume of the cake is - π4²D => 16πD


Now Jules wants to keep the Depth of the container the same and wants to increase the diameter to 12 Inches ( probably he has invited some other people for the party) , so the radius of the proposed cake will be 6 inches.

So , Volume of the cake proposed to be bakes is = π6²D => 36πD


So , Jules must mix the ingredients in the ratio of New Volume / Actual Volume according to Recipe

For baking the desired diameter of Cake Jules must now multiply his ingredients by -

=> 36πD / 16πD => 9/4 = 2 and 1/4th

Hence Answer will be (B)

A general approach that will work no matter what numbers you have:

Volume/area of new cake
-----------------------
Volume/area of old cake

In this case, the "area" (shouldn't this be a 3D cake? Oh well ...) of the old cake is πr², or π*4², or 16π. The area of the new cake is π*6² = 36π. 36π / 16π = 2.25, and you're done - that's the factor by which you'd have to multiply.