Question

changing dimensions in a rectangular box

suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates:

dx/dt = 1 m/sec, dy/dt = -2 m/sec, dz/dt = 1 m/sec

find the rates at which the box's (a) volume, (b) surface area, and (c) diagonal length s = (x^2 + y^2 + z^2)^(1/2) are changing at the instant when x = 4, y = 3, and z = 2