A cone-shaped paper drinking cup (like the kind used at water fountains) has a r

Question

A cone-shaped paper drinking cup (like the kind used 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 V = 1/3 pi (R/H)2 h3 Suppose that the cup's dimensions are R = 1.5 in. and H = 4 in. If the flow rate from the fountain into the cup is 2 in.3/sec, use Simulink to determine how long will it take to till the cup to the brim. If the flow rate from the fountain into the cup is given by 2(1 - e -2t) in.3/sec, use Simulink to determine how long will it take to fill the cup to the brim.

Explanation / Answer

for cup to fill upto brimm ewe have
h=H
a)2*t=(1/3)(1.5/4)^(2)*4^(3)

=>2t=(1/3)*2.25*4

=>6t=10

=>t=5/3 sec

b)2(1-e^(-2t))t=(1/3)(1.5/4)^(2)*4^(3)

=10/3

=>t(1-e^(-2t))=5/3

t=5.25 sec

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