Problems 1. Peter pours water into a leaky tank at a rate of 10 m per hour. The tank is a cone with vertex down, with 9 m in depth and 6 m in diameter at its top. When the depth is 6 m, the surface of water in the tank is rising at a rate of 20 cm per hour. Find the rate that the water is leaking out at that time instant. 2. Consider a 10 m long ladder, with one end on the ground. The ladder is being supported partway along its length, by positioning on top of a 3 m high fence, as illustrated in the following figure. If the bottom of the ladder is 4 m from the base of the fence, and is being dragged along the ground way from the fence at a rate of 02 m per second. (a) How fast is the free top end of the ladder moving in vertical manner? (b) How fast is the free top end of the ladder moving in horizontal manner? Show all steps. 10 m 3 m 1/5 m/'s 3. Among all isosceles triangles of given perimeter, using Calculus, determine the type of triangle that has the greatest area. Show your set-up, and steps of derivation