A crystal is in the shape of a cube. Each edge is growing at the rate of .20 millimeter per minute. Find the rate of change of the volume when each edge is of length 3.0 millimeter.

I need help with this one. Answer is 5.4 mm/min. But I don't know how to solve it.

Question

A crystal is in the shape of a cube. Each edge is growing at the rate of .20 millimeter per minute. Find the rate of change of the volume when each edge is of length 3.0 millimeter.

I need help with this one. Answer is 5.4 mm/min. But I don't know how to solve it.

irishboy123 · Answer

$$V = l^3$$
you know dl/dt
$$\frac{dV}{dt} = ?$$

moonlight93 · Answer

@IrishBoy123. You mean the derivative?  Or distance= Velocity/time. I still don't get it?  Please help if you can.

irishboy123 · Answer

V = volume
l = length
t = time
dV/dt and dV/dl are the derivatives

moonlight93 · Answer

Ok, but how did they get 5.4 mm/min? Idk how to set it up.

irishboy123 · Answer

dV/dt = dV/dl • dl/dt  ???

irishboy123 · Answer

that mean anything to you?

akashdeepdeb · Answer

You need to know the basic concept of derivatives for this. Try watching these videos: https://www.youtube.com/watch?v=Ji_9bJdA_g8&list=PLIxD98N749bPWrcJbQcxxXbOZtQIQfh8b

moonlight93 · Answer

I know derivatives; I know the product constant rule, power rule, sum rule, quotion rule, exponential and logs rule, and a little bit about chain rule. I posted this question because although I know some  about 'Derivatives' I was never in a situation to solve a word problem derivitive.  I posted this question because I wasn't able to do it. Thank you though.