# Thread: How long is a piece of string?

1. ## How long is a piece of string?

Hey guys,

I am seriously stuck on how to answer this question.

Any tips on how to answer these questions would be greatly appreciated!

Please see the image below:

my attempt is that the length of string is 4x + 4y, but I feel like I am incorrect as it is not in terms of x. I'm just overall really stuck.

2. ## Re: How long is a piece of string?

looking at the diagram it appears that

$L(x) = 4x+4y$

which is what you got.

We're told the volume $V = 8000~cm^3$

$V = x^2 y$

$y = \dfrac{V}{x^2} = \dfrac{8000}{x^2}$

$L(x) = 4x + \dfrac{32000}{x^2}$

can you proceed from here?

3. ## Re: How long is a piece of string?

Hi there romsek,

thankyou so much!

is the dL/dx just asking me to differentiate the L(x)=4x+(32000/x2)

4. ## Re: How long is a piece of string?

Originally Posted by ifailedmaths
Hi there romsek,

thankyou so much!

is the dL/dx just asking me to differentiate the L(x)=4x+(32000/x2)
yep