Water is leaking out of an inverted conical tank at a rate of 6000 cm3/min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 m and the diameter at the top is 4 m. If the water level is rising at a rate of 20 cm/min when the height of the water is 2 m, find the rate at which water is being pumped into the tank.
* I am confused as to whether i should derivate with respect to the radius or height of the volume, or implicitly.
Two sides of a triangle have lengths 4 m and 12 m. The angle between them is increasing at a rate of 0.06 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is 60°.
* I tried assuming i could use one of the trigonometric functions but I could not figure out where to go afterwards.