related rates prob: how fast is the surface area increasing?

[skacat330]

I am doing a related rates problem and I have no idea how to set it up. I haven't been able to find any examples in my book, notes or web on this one. I need help setting this up.

"The volume of a cube is increasing at a rate of 10cm^3 per minute. How fast is the surface area increasing when the length of an edge is 30 cm."

Any help as soon as possible would greatly be appreciated. :?: :?

 

[skeeter]

The volume of a cube is increasing at a rate of 10cm^3 per minute

dV/dt = 10 cm³/min

How fast is the surface area increasing when the length of an edge is 30 cm.?

they want dA/dt when s = 30 cm

equations needed ...
volume of a cube, V = s³
surface area of a cube, A = 6s²

d/dt[A = 6s²]
dA/dt = 12s(ds/st)
to find dA/dt ... you have s, but need the value of ds/dt.

d/dt[V = s³]
dV/dt = 3s²(ds/dt)
you have dV/dt and s ... you can solve for ds/dt, then you can determine dA/dt.

 

[skacat330]

thanks that really helps! I am so glad you replied quickly.