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A certain cake recipe states that the cake should be baked in a pan 8

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A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

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New post 07 Dec 2017, 04:36
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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 1/2
(B) 2 1/4
(C) 1 1/2
(D) 1 4/9
(E) 1 1/3

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A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

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New post Updated on: 07 Dec 2017, 08:41
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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 only

A 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

Originally posted by generis on 07 Dec 2017, 08:11.
Last edited by generis on 07 Dec 2017, 08:41, edited 2 times in total.
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A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

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New post 07 Dec 2017, 08:25
2
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




Hi genxer123
even the round pan will give you an answer..
round pan means it is cylinderical and by increasing diameter we are increasing the VOLUME..

volume of cylinder is \(pi*r^2h\)....
here radius are \(\frac{12}{2}=6\) and \(\frac{8}{2}=4\)
ans = \(\frac{V_{12}}{V_8} = \frac{pi*6^2*h}{pi*4^2*h}=\frac{36}{16}=\frac{9}{4}=2\frac{1}{4}\)

B
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A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

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New post 07 Dec 2017, 08:37
chetan2u wrote:
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




Hi genxer123
even the round pan will give you an answer..
round pan means it is cylinderical and by increasing diameter we are increasing the VOLUME..

volume of cylinder is \(pi*r^2h\)....
here radius are \(\frac{12}{2}=6\) and \(\frac{8}{2}=4\)
ans = \(\frac{V_{12}}{V_8} = \frac{pi*6^2*h}{pi*4^2*h}=\frac{36}{16}=\frac{9}{4}=2\frac{1}{4}\)

B

I stand corrected. My arithmetic was off on the round pan. Nice catch - thanks!
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Re: A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

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New post 07 Dec 2017, 09:13
84pi/40 pi

my ans is 2.1 closest to B but why isnt it just the same??
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A certain cake recipe states that the cake should be baked in a pan 8  [#permalink]

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New post 07 Dec 2017, 11:09
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

nabiharaza wrote:
84pi/40 pi

my ans is 2.1 closest to B but why isnt it just the same??

nabiharaza , I think your arithmetic might be incorrect, but I can't tell because I don't have your steps. How did you get \(84\pi\) and \(40\pi\)?

Let's say you want to take the changed volume approach (you can just check changed area, see my post above).

Choose any height for the round pan. It does not change. Let h = 3

A circular pan with an 8-inch diameter has a radius of 4 inches. Its volume, that of a cylinder:

\(\pi r^2h = \pi(16)(3) = 48\pi\)

A circular pan with a 12-inch diameter has a radius of 6 inches. h = 3. Its volume is

\(\pi r^2h = \pi(36)(3) = 108\pi\)

Increase factor?
\(\frac{108\pi}{48\pi}=\frac{9}{4}\) (divide LHS by 12)

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

I hope that helps. If not, please show your steps? :-)
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