Keith Brymer (from The Great Pottery Throwdown) is working in the pottery studio.

(a) He begins by making a coiled pot, which is formed out of long "snakes" of clay which are coiled around to create the pot. He pulls out a 1kg lump of clay and begins to roll it into a long thin cylinder. As he rolls it, it gets longer and skinnier. When it is 45cm long and has a radius of 2cm, the length is increasing at 10cm per minute. How fast is the radius changing at that instant?

(b) For his second project, Keith uses the pottery wheel to turn a lump of clay into a cylindrical vase. Before glazing it, he leaves it to dry in the drying room, during which time the clay shrinks. If the radius of the vase shrinks at a rate of 1cm per day and the height shrinks at a rate of 0.5cm per day, at what rate does the volume of the vase shrink when the radius is 5cm and the height is 12cm?