The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge of the cube changing when the edges are 6 in long? (Recall t

Question

The volume of a cube is increasing at a rate of 60 in3/sec. At what rate is the length of each edge of the cube changing when the edges are 6 in long? (Recall that for a cube, V = x3.) 

Answer 1

Related rates means you're usually going to have to take the derivative of your formula implicitly (in terms of another variable that's not part of the formula).  In this case we want to take the derivative in terms of time, t.

 

So if V = x³

then dV/dt = 3x² (dx/dt)    

 

Now the question tells us what the rate of the volume is, so that's DV/dt, and it also tells us the side length, so that'll be x.

Plug in and solve for dx/dt, the rate at which sides are increasing.