The length ℓ, width w, and height h of a box change with time. At a certain instant the dimensions are ℓ = 4 m and
w = h = 1 m,
and ℓ and w are increasing at a rate of 2 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the following quantities are changing.
(a) The volume.
m3/s
(b) The surface area.
m2/s
(c) The length of a diagonal. (Round your answer to two decimal places.)
m/s