physics question

[rinsterman12]

cells can only absorb nutrients through their surfaces. In , order for a cell to absorb nutrients most efficiently, it will grow to a max size and divide. If the total volume remains constants when a cell divides, then the ratio of the surface areas of the daughter cells to the original is?
In the passage is states L or length is prop. to L^2, surface area, which in turn is proportional to L^3. I do not understanrd why the ratio would not be 2^2/1. The ratio is 2^1/3/1. It has something to do with L^3= 2L^3. I dunno i am totally lost please help

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[SoftwareKevin]

cells can only absorb nutrients through their surfaces. In , order for a cell to absorb nutrients most efficiently, it will grow to a max size and divide. If the total volume remains constants when a cell divides, then the ratio of the surface areas of the daughter cells to the original is?
In the passage is states L or length is prop. to L^2, surface area, which in turn is proportional to L^3. I do not understanrd why the ratio would not be 2^2/1. The ratio is 2^1/3/1. It has something to do with L^3= 2L^3. I dunno i am totally lost please help

Let's call Surface Area SA and Volume V

SA ~ L^2
V ~ L^3

From that we can say
L ~ V^(1/3)

If volume is halved, length is now proportional to (1/2)^(1/3)

Since SA ~ L^2, we can say SA for each cell is proportional to (1/2)^(2/3).

We have two cells... so the total surface area is proportional to 2*(1/2)^(2/3) = ((1/2)^-1)*((1/2)^(2/3)) = (1^2)^(-1/3) = 2^(1/3)

Thus we get our ratio of new total surface area to old total surface area as 2^(1/3) to 1

The key is initially figuring out what the new length is based on half volume. Then it's just math tricks to get the answer into the right form.

 

[Phantastic]

I don't understand that math trick...is that really necessary? Will the MCAT require that I be able to perform this trick?

edit: nvm now I see what you did. Still looks a bit more than what MCAT would expect from me, no? Usually we're just comparing relationships when it comes to proportionalities...not comparing and formatting elegeantly.

 

[SoftwareKevin]

I don't understand that math trick...is that really necessary? Will the MCAT require that I be able to perform this trick?

You should be comfortable doing something like:
x^-1 = 1/x

The way I solved it I had x*((1/x)^something). I needed the things I was multiplying to together to both be in the form x^something or (1/x)^something so that I could add just add exponents to solve for a final value.

Maybe there's another way to go about solving the problem, but at least the way I worked it out I had to play around with the numbers to get them into a form that matched the answers.