Answer to Question #331612 in Calculus for nick

Question

The length l, width w, and height h of a rectangular box (with a lid) change with time. At a certain instant the dimensions are l= 10 m, w= 5 m, h= 2 m, and l and w are increasing at a rate of 10 m/s while h is decreasing at a rate of 10 m/s.

find

Suppose S

 is the surface area of the box. At the relevant instant: 

∂h/∂t=

∂S/∂l=

∂S/∂w=

  

The rate at which the surface area of the box is changing at that instant is: