Edit: my answer to the first question is wrong. See Jhevon's post for the correct method.
This question is confusing because you are given more information than you need. All you have to do is follow the normal procedure and ignore some of it.Water runs into a tank that is in the shape of an inverted cone at the rate of 9cubic feet/min. The tank has a height of 10 ft and a base radius of 5 ft. How fast is the water level rising when the water is 4 ft deep?
. You want and have . Implicit differentiation looks easiest for finding , but if you haven't done that yet you can just rearrange.The length of the base of a right triangle is increasing at the rate of 12in/min. At the same time, the height of the triangle is decreasing in such a way that the length of the hypotenuse remains 10 inches. How quickly is the height of the triangle changing when the length of the base is 6 inches?
A spherical balloon is being inflated so that its volume is increasing at the rate of 5 cubic meters/min. At what rate is the diameter increasing when the diameter is 12m? (V = 4/3(pi)r^3)