How do you do this problem?

Question

a rectangular prism with dimensions l*w*h is expanding its length and width by4m/min and 3m/min respectively, while keeping the height the same how fast is the volume of the prism changing when its dimension is 5m*4m*7m?

Answer 1

V = L * W * h

 

dV =  (L * dW + dL * W )* h <--- product rule with fixed constant h

 

     = (5 * 4 + 3*4 )* 7 = (20 + 12)*7 = 32 * 7 = 224