Year 12s: what will be the first way you research your future options? >>

C3 question

Question:
A spherical balloon has radius r cm has volume Vcm^3 where V=4/3(pi)^3.

The balloon is infalted at constant rate of 10cm^3 per sec. Find the rate of increase when r=8.

I found the answer for this question (cred. to Kool_Panda) :

dv/dr = 4*pi*r^2
dv/dt = (dv/dr)*(dr/dt)
10 = (4*pi*64)*(dr/dt)
dr/dt = 10/(256*pi) = 0.0124

Can someone explain this to me please? I do know how to differentiate, but can't understand the meaning of it.

Reply 1

TenOfThem

Original post by Hody421

What part don't you understand

Reply 2

Hody421

Original post by TenOfThem

What part don't you understand

I don't understand why we have to differentiate the formula for the volume of sphere in the first place.

The rest seems pretty clear, as I understand t=time.

Reply 3

TenOfThem

Original post by Hody421

I don't understand why we have to differentiate the formula for the volume of sphere in the first place.

The rest seems pretty clear, as I understand t=time.

Can you give the actual question please

Based on the answer it would appear that you are looking for the rate at which the radius is increasing but your OP does not say that

Reply 4

Hody421

Original post by TenOfThem

Can you give the actual question please

Based on the answer it would appear that you are looking for the rate at which the radius is increasing but your OP does not say that

http://www.thestudentroom.co.uk/attachment.php?attachmentid=296424&d=1402950795

Question no.5

Reply 5

TenOfThem

Original post by Hody421

http://www.thestudentroom.co.uk/attachment.php?attachmentid=296424&d=1402950795

Question no.5

ok

The fact that you did not give the correct question suggests that you do not really understand this topic

Do you know what is meant by

Rate of change of r

\dfrac{dr}{da}

\dfrac{da}{dr}

Inflated at a constant rate of .....

Reply 6

the bear

these are all about setting up a suitable chain...

to find d&/dt

you write

d&/d? x d?/dt

one of the two parts of the chain will be a fixed amount such as 12 cm/sec

the other one you get by differentiating a formula...

for instance if you need dr/dv for a sphere you first find dv/dr by differentiating 4/3π r³ with respect to r...

Reply 7

prowster

If you were to plot the graph of volume against time, you would use the V=4/3piR^3. Similarly if you were to plot displacement against time on a graph, you would use velocity=d/t.

The question is asking for the time where the rate of change = 8.
When you differentiate anything, you get an equation to work out the rate of change of the variable. So if you were to differentiate an equation which gives you velocity, you would end up with an equation which gives you acceleration because acceleration is the rate of change if velocity.

So when you differentiate the volume of the Balloon equation, you are getting an equation which tells you how fast the volume of the balloon is increasing, at any given time.

Posted from TSR Mobile

Reply 8

Hody421

Original post by TenOfThem

ok

The fact that you did not give the correct question suggests that you do not really understand this topic

Do you know what is meant by

Rate of change of r

\dfrac{dr}{da}

\dfrac{da}{dr}

Inflated at a constant rate of .....

Erm, not really. :s-smilie:

what is dA?

Reply 9

TenOfThem

Original post by Hody421

Erm, not really. :s-smilie:

what is dA?

Ok

So you do not really understand the basics of differentiation from C1 and C2 - I suggest that rather than worrying about C3 differentiation you go back to basics and learn what differentiation is about so that you understand what these questions are asking

You could use the information that people will give you on here about using the chain rule etc and get your homework right but that would not help your general understanding - I suggest that you talk to your teacher and ask them to take you through this