C4 Differentiation Question

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

Reply 2

the bear

20

what have you done so far Kate ?

:holmes:

Reply 3

OP

Original post by the bear

what have you done so far Kate ?

:holmes:

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 :frown:

Reply 4

OP

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

Reply 5

freddster1018

are you sure it's KA^0.5? I got an answer for KA^-0.5

Reply 6

OP

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?

Reply 7

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?

Reply 8

OP

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

Reply 9

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

Reply 10

OP

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

Reply 11

Original post by katerobertsonxx

that's where i got confused, A= 6x² and V= x³

So what is x in terms of v

Reply 12

username1732491

18

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.

Moved to maths.

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.

(edited 8 years ago)

Reply 15

OP

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

Reply 16

OP

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?}

Reply 17