A cylindrical container of radius 8cm and height 25cm is completely filled with water.
The water is then poured at a constant rate from the cylinder into an empty inverted cone.
The cone has radius 15cm and height 24cm and its axis is vertical.
It takes 40 seconds for all of the water to be transferred.
a. If V represents the volume of water, in cm3, in the cone at time t seconds, find dV/dt in terms of π.
b. When the depth of the water in the cone is 10 cm, find:
i. the rate of change of the height of the water in the cone
ii. the rate of change of the horizontal surface area of the water in the cone.