A rectangular prism has its length increasing by 12 cm/min, its width increasing by 4 cm/min and its height increasing by 2 cm/min. How fast is it's volume changing when the dimensions are 200 cm in length, 50 cm in width and 30 cm in height?

The following is my working:

dL/dt = 12 cm/min

dW/dt = 4 cm/min

dH/dt = 2 cm/min

V = L x W x H

we get:

V=(200+12t)(50+4t)(30+3t)

$\displaystyle V = 144t^3 + 5460t^2 + 72000t + 300,000$

Derivative of V

$\displaystyle V' = 432t^2 + 10920t + 72000$

Now, I'm very confused. How could we find the rates of change,when 200 cm in length, 50 cm in width and 30 cm in height?

Thanks!