Question

Suppose the length of a rectangular box, with lengths x,y,z are changing at the following rates

dx/dt = 2 cm /sec
dy/dt = -3 cm /sec
dz/dt = 1 cm/ sec

when x =4, y=3 z=2,

Find

i) Rate at which volume is changing wrt time,

ii) Rate at which the diagonal length of the box is changing wrt time.


My answers are

i)0
ii) 1/root(29)

Can anyone help me verify if this is correct?