Originally Posted by freswood
Get the value of a from first equation
Divide equation 3 by equation 2
You will get the answer
At first this question seemed easy, however I still can't get the answer. I've been using the formula:
dx/dt = dx/dy * dy/dt
The surface area of a cube is changing at the rate of 8cm^2/second. How fast is the volume changing when the surface area is 60 cm?
Thanks for your help
I am sorry but I don't want to give you a solution straightaway.Originally Posted by freswood
Answer these simple questions and solve the problem yourself.
1)What do you intend to find?Write down an expression for it.
2)I am listing a few things. Tell whether you can find their value, if yes, what is their value:
3)Write an expression for dV/dt. What values do you need for it?Can you find those values in ques.2?
I hope that you can solve the problem now. I still you have any problem, post it and i will try to tell you, straightaway this time.
To find dy/dx . There are two cases(for explicit functions):you want to find dy/dx in terms or yuo want to find dy/dx in terms of y.
To find in terms of x, express y as a function of x and differentiate.
to find in terms of y, express x as a function of y and differentiate.
1) dV/dtOriginally Posted by malaygoel
S = 6a^2 where a is side length
a = 10^.5
V = a^3
dS/dt = 8
dS/da = 12a
dV/da = 3a^2
3) For dV/dt you need dx/dt and dS/dV
But that's the whole problem - I don't know how to find dS/dV. I know you think you're doing the right thing, and I appreciate your help, but I like to be able to work backwards. This question is causing me a lot of grief. I'm doing maths a year ahead, and I find it hard to keep up with the older girls.
I think (but am probably wrong) the problem here is that x,t,and yOriginally Posted by freswood
in dx/dt = dx/dy * dy/dt, are serving as place holders for whatever is
relevant to the problem at hand.
For this problem you replace x by V (representing the volume of the
cube) and y by S (representing the surface area of the cube) and let
t represent time. Then your ralation between derivatives becomes:
dV/dt=dV/dS * dS/dt.
You are told dS/dt=8 (cm^2/s), so you need to find dV/dS.
The volume V of a cube of side a is a^3, and the surface area of
such a cube is 6a^2, so expressing V in terms of S gives:
and the rest should be plain sailing.