A cone-shaped paper drinking cup (like the kind supplied at water fountains) has a radius R and a height H. If the water height in the cup is h, the water volume is given by
Suppose that the cup’s dimensions are R = 1.5 in. and H = 4 in.
a. If the flow rate from the fountain into the cup is 2 in. 3/s, how long will it take to fill the cup to the brim?
b. If the flow rate from the fountain into the cup is given by 2(1 – e–2t) in.3/s, how long will it take to fill the cup to the brim?