(5) (12 points) The length of a rectangle is increasing at a rate of 5 cm/sec while the width of the
rectangle is decreasing at a rate of 2 cm/sec. Find the rate of change of the area of the rectangle at
the moment that the length is 20 cm and the width is 10 cm. Is the area increasing or decreasing at
this moment?
(6) (12 points 6 each) A grain silo is to be made into the shape of a right circular cylinder of radius
r and height h surmounted by a hemisphere with the same radius r. The volume V is given by
V = πr2 h + 32 πr3 . Suppose that the values of r, h and V may change in time.
(a) Find
dV
dt
in terms of
dh
dt
if r is a constant.
(b) Find
dV
dt
in terms of
dr
dt
if h is a constant.
(6) (15 points) A boat is pulled into a dock by a rope attached to the bow of the boat passing
through a pulley on the dock that is 1 m higher than the bow of the boat. If the rope is pulled in at
a rate of 1 m/sec, how fast is the boat approaching the dock when it is 8 m from the dock?