An hourglass is made up of two glass cones connected at their tips. Both cones have radius 1 inch and height 3 inches. When the hourglass is flipped over, sand starts falling to the lower cone.

a. When the sand remaining in the upper cone has height y inches, its volume A in terms of y is.
b. When the sand in the lower cone has reached a height of h inches, its volume B in terms of h is . (Hint: B is the volume of the bottom cone minus the volume of the empty space above the sand.)
c. Assume the total volume of sand in the hourglass is 3π/4 cubic inches. Also, assume the height of the sand in the upper cone is decreasing at a rate of 12/100 inches per second. At the instant when the sand in the lower cone is 1 inch high, the height of the sand in the lower cone is increasing at a rate of inches per second.