Water is being poured into a conic tank at a constant
rate. The conic tank is 12 feet deep and has a radius of
6 feet at the top as shown. The volume of a cone with
height h and radius r is know to be

and the equtious given V=1/3pir^2h

ii. Find the volume of the lled portion of the tank as
a function of its height.
iii. Find the rate the height of the water is increasing,
dh/dt .

Question

Water is being poured into a conic tank at a constant
rate. The conic tank is 12 feet deep and has a radius of
6 feet at the top as shown. The volume of a cone with
height h and radius r is know to be


and the equtious given V=1/3pir^2h


ii. Find the volume of the lled portion of the tank as
a function of its height.
iii. Find the rate the height of the water is increasing,
dh/dt .