Everyone has seen the old, cliche related rates problem where a cone is being filled with water. How fast is the height of the water changing at the instant the water is h units deep...yada, yada?.
In these problems, the apex of the cone is always pointed down.
What if the cone were laying on its side?. Makes it a little tougher, huh?.
Suppose we have a conical tank with radius 10 ft and height 24 feet. Water is flowing in at 20 ft^3 per minute. How fast is the depth increasing when the water is 6 feet deep?. Only the cone is on its side, not apex down.