A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at the rate of 10 cubic feet per minute, find the rate of change of the depth of the water the instant it is 8 feet deep? 1 V · Trh 3

Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always four times its height. Suppose the height of the pile increases at a rate of 1 cm/s when the pile is 13 cm high. At what rate is the sand leaving the bin at that instant? Let V and h be the volume and height of the cone, respectively. Write an equation that relates V and h and does not include the radius of the cone. (Type an exact answer, using n as needed.) Differentiate both sides of the equation with respect to t. dV dh %3D dt dt (Type an exact answer, using n as needed.) The sand is leaving the bin at a rate of (Type an exact answer, using a as needed.)