[quote]1)An oil storage tank has the shape of a paraboloid with a radius of 5ft and a height of 9ft. Oil flows into the tank at the rate of 8 cubic feet/min. The volume of the tank is V=(50*pi*h^(3/2))/3.
a)Find the volume of a full tank
b)How long would it take to fill the tank if it was initially empty?
c)How fast is the height of oil increasing when h=4?
For part a, just use h=9 in V to find the full volume.
part b, Use the given 8 cubic feet/min and the result from part a.
part c, Use h=4 and dV/dt=8 and solve for dh/dt
Use similar triangles to eliminate a variable. This problem is an old cliche related rates. If you google you will probably find something similar.2)A container has the shape of an open right circular cone. The height of the container is 10cm and the diameter or the opening is 10cm. Water in the container is evaporating so that its depth, h, is changing at a constant rate of -3/10 cm/hr.
a)Find the volume V of water in the container when h=5 cm.
b)Find the rate of change of the volume of water in the container, with respect to time, when h=5 cm.
Now, sub into the volume of cone formula, differentiate to get dV/dt. Then, enter in your h=5 to find dV/dt at that height. You are given dh/dt=-3/10