Answer to Question #64601 in Calculus for Justine

Question

10. The height of a rectangular box is increasing at a rate of 2 meters per second
while the volume is decreasing at a rate of 5 cubic meters per second. If
the base of the box is a square, at what rate is one of the sides of the base
decreasing, at the moment when the base area is 64 square meters and the
height is 8 meters?

11. Sand is pouring out of a tube at 1 cubic meter per second. It forms a pile
which has the shape of a cone. The height of the cone is equal to the radius of
the circle at its base. How fast is the sandpile rising when it is 2 meters high?

12. A water tank is in the shape of a cone with vertical axis and vertex downward.
The tank has radius 3 m and is 5 m high. At first the tank is full of water,
but at time t = 0 (in seconds), a small hole at the vertex is opened and the
water begins to drain. When the height of water in the tank has dropped to
3 m, the water is flowing out at 2 m3/s. At what rate, in meters per second,
is the water level dropping then?