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

skacat330

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Jul 15, 2006
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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. :?: :?
 
The volume of a cube is increasing at a rate of 10cm^3 per minute
dV/dt = 10 cm<sup>3</sup>/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 = s<sup>3</sup>
surface area of a cube, A = 6s<sup>2</sup>

d/dt[A = 6s<sup>2</sup>]
dA/dt = 12s(ds/st)
to find dA/dt ... you have s, but need the value of ds/dt.

d/dt[V = s<sup>3</sup>]
dV/dt = 3s<sup>2</sup>(ds/dt)
you have dV/dt and s ... you can solve for ds/dt, then you can determine dA/dt.
 
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