I have tried to follow this thread and your previous posts and have still not figured out exactly what the original problem was. It seems that you have been going along for a while now on this problem.

I think that if you posted a more concise definition of the original problem that you would be pleasantly surprised by a more simple solution. It sounds like some type of basic related rate problem which ususally can be solved quite simply with all of the relevant information from the beginning.

Forgive me if I sound like some type of a-hole, but I think that you somehow made this problem more difficult than it truly needs to be. I, and I suspect others here, would love to help you, but your problem never seemed to be exactly clear from the beginning.

]]>= Pi* R * S where S= Square root of H^2 + R^2

U know i was doing a question for truncated cone.........so what i did was i put some dotted lines on that truncated cone to make it like a cone and i said that the dotted lines were 1/3 of the whole cone, as i wanted to find the surface area, meaning the radius is 1/3, height is 1/3 and slant height (s) is 1/3. So can we write:

= Pi * R/3 * Square root of R^2 + H^2 / 3 ???? (note: 3 is not in square root, its seperate)

In simple numbers i have done : Pi*r/3*s/3

I hope u understand the problem????

]]>I had volume fixed to 600cm^3.

Then i substituted the equation of height into the surface area. It came to something like this:

S.A= Pi*R * square root of R^2 + 2025/Pi*R^2

Then i had to subtract this equation by 1/3 R and 1/3 of H, when i simplified it came to the equation which i gave u!!!!! .

Hope u understand. And thanks once again.

]]>y = (pi^2 r^6 + 4100625)^(1/2) / r - (pi^2 r^6 + 36905625)^(1/2) / 3r

There are no shortcuts here and the answer will not be pretty. It is easier if you treat each part of this equation as a separate function and then add them back together after differentiating.

We will call the first part A and the second part B. Also the constants have no effect upon the outcome so we will call them a and b respectively.

A = (pi^2 r^6 + a)^(1/2) / r = [(pi^2 r^6 + a) / r^2)]^(1/2)

dA/dr = {1/2 [(pi^2 r^6 + a) / r^2]^(-1/2)} {[(6 pi^2 r^5)r^2 - 2r(pi^2 r^6 + a)] / r^4}

dA/dr = (6 pi^2 r^7 - 2 pi^2 r^7 - 2ar) / [(4 pi^2 r^14 + 4a r^8) / r^2]^(1/2)

dA/dr = (4 pi^2 r^7 - 2ar) / [4 pi^2 r^12 + 4a r^6]^(1/2)

da/dr = (4 pi^2 r^7 - 2ar) / 2 r^3 [(pi^2 r^6 + a)^(1/2)]

da/dr = (2 pi^2 r^6 - a) / (pi^2 r^10 + a r^4)^(1/2)

B = (pi^2 r^6 + b)^(1/2) / 3r = [(pi^2 r^6 + b) / 9 r^2]^(1/2)

db/dr = {1/2[(pi^2 r^6 + b)/(9 r^2)]^(-1/2)}{[6 pi^2 r^5(9 r^2) - 18r(pi^2 r^6 + b)]/81 r^4}

db/dr = (54 pi^2 r^7 - 18 pi^2 r^7 + 18br)/[54 r^3(pi^2 r^6 + b)^(1/2)]

db/dr = (36 pi^2 r^7 + 18br) / [54 r^3(pi^2 r^6 + b)^(1/2)]

db/dr = (2 pi^2 r^6 + b) / [3 r^2 (pi^2 r^6 + b)^(1/2)]

whew....

dy/dr = {(2 pi^2 r^6 - a) / (pi^2 r^10 + a r^4)^(1/2)}

- (2 pi^2 r^6 + b) / [3 r^2 (pi^2 r^6 + b)^(1/2)]

This is why you have not gotten any answers. It is too long a computation just for the sake of argument. I have just found the rate of change for an unknown function. It is pretty dissatisfying.

Perhaps you could tell us what the function represented.

]]>You will need to use the chain and quotient rules. Here are the pieces:

[ (π² * r^6 + 4100625)² ]′ = 2( π² * r^6 + 4100625 ) * 6π²r^5

= 12π²r^5(π² * r^6 + 4100625)

Quotient rule the first bit:

{ r * [ 12π²r^5(π² * r^6 + 4100625) ] - (π² * r^6 + 4100625)² } / r²

Now for the second bit:

[ (π² * r^6 + 36905625)² ]′ = 12π²r^5( π² * r^6 + 36905625)

{ 3r * 12π²r^5( π² * r^6 + 36905625) - 3(π² * r^6 + 36905625)² } / 9r²

Put them together:

( { r * [ 12π²r^5(π² * r^6 + 4100625) ] - (π² * r^6 + 4100625)² } / r² ) - ( { 3r * 12π²r^5( π² * r^6 + 36905625) - 3(π² * r^6 + 36905625)² } / 9r² )

I'm sure you could simplify that quite a bit, but it's hard to see on a computer screen.

]]>= Square of Pi^2*r^6 + 4100625 / r - Square of Pi^2*r^6 + 36905625 / 3r.

*Note that the r and 3r dividing the square of above expression are not in square, they are seperate and just dividing.*

Please help.

]]>