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# C4 Differentiation Question watch

1. At time 'T', the surface area of a cube is Acm^2 and it's volume is Vcm^3. The volume of the cube is expanding at a uniform rate of 2cm^3s^-1. Show that dA/dT = KA^-0.5 where K is a constant to be determined.

2. (Original post by katerobertsonxx)
At time 'T', the surface area of a cube is Acm^2 and it's volume is Vcm^3. The volume of the cube is expanding at a uniform rate of 2cm^3s^-1. Show that dA/dT = KA^0.5 where K is a constant to be determined.
how can you relate the volume of the cube to the surface area
3. what have you done so far Kate ?

4. (Original post by the bear)
what have you done so far Kate ?

nothing im struggling to even get started, i missed this lesson and nobody has clear notes and the teachers not been in for a while unwell
5. (Original post by samb1234)
how can you relate the volume of the cube to the surface area
i have no idea, i've been researching and everything includes an equation for the side length but i've not been given it so i'm really stuck
6. are you sure it's KA^0.5? I got an answer for KA^-0.5
7. (Original post by freddster1018)
are you sure it's KA^0.5? I got an answer for KA^-0.5
oops maybe it would help if i wrote the question down right! yeah it is -0.5 sorry! how'd you manage it?
8. (Original post by katerobertsonxx)
i have no idea, i've been researching and everything includes an equation for the side length but i've not been given it so i'm really stuck
sin(2x) let 2x =u, dy/dx =dy/du x du/dx . Can we use a similar thing here?
9. (Original post by samb1234)
sin(2x) let 2x =u, dy/dx =dy/du x du/dx . Can we use a similar thing here?
not sure i had dA/dV x dV/dT but then got stuck
10. (Original post by katerobertsonxx)
not sure i had dA/dV x dV/dT but then got stuck
You are along the right lines. How could we express A in terms of V so we can find da/dv
11. (Original post by samb1234)
You are along the right lines. How could we express A in terms of V so we can find da/dv
that's where i got confused, A= 6x2 and V= x3
12. (Original post by katerobertsonxx)
that's where i got confused, A= 6x2 and V= x3
So what is x in terms of v
13. (Original post by katerobertsonxx)
i have no idea, i've been researching and everything includes an equation for the side length but i've not been given it so i'm really stuck
It's a very simple and easy comparison which you would be better working out for yourself than looking up online - it shouldn't take too long (it's a cube for crying out loud).

You sound like you need a break. Go for a walk and get a snack or something and come back to it when you're feeling calmer. Getting stuck on simple problems like this is normal and it's happened to me many times before. Just take a f*cking break.
14. Moved to maths.
15. You could find A in terms of V or you could just leave A and V in terms of x and then do it by finding dA/dx and dV/dx and then manipulating to get dA/dT.
I think finding A in terms of V is the better option though.
16. (Original post by B_9710)
You could find A in terms of V or you could just leave A and V in terms of x and then do it by finding dA/dx and dV/dx and then manipulating to get dA/dT.
I think finding A in terms of V is the better option though.
thankyou
17. (Original post by samb1234)
So what is x in terms of v
I have had a go and I am even more confused now as I have no K anywhere,

I have written down:

Area= 6x2
Volume= x3

dA/dX= 12x
dV/dX= 3x squared

dA/dT= da/dX x dX/dV x dV/dT

= 12x x 1/3x squared x 1/2 V to the power 1/3?

am I completely going the wrong way?
18. (Original post by katerobertsonxx)
I have had a go and I am even more confused now as I have no K anywhere,

I have written down:

Area= 6x2
Volume= x3

dA/dX= 12x
dV/dX= 3x squared

dA/dT= da/dX x dX/dV x dV/dT

= 12x x 1/3x squared x 1/2 V to the power 1/3?

am I completely going the wrong way?
you are trying to find k. K is just some constant e.g. 5,10, 4 etc i.e. it's just the coefficient of the A-^0.5 term
19. am I too late?
20. (Original post by TeeEm)
am I too late?
nope never too late haha still not finished it i just cant get my head around it

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