Related Rates 1. A water tank is in the form of a right circular cone with vertex down, 12 ft. deep and 6 feet across the top. Water is being pumped into the tank at the rate of 10 ft/min. How fast is the surface of the water in the tank rising when the water is 5 ft. deep? 2. A helicopter is rising vertically from the ground at constant rate of 15 ft/s. When it is 250 ft. off the ground, a jeep passed beneath the helicopter travelling in a straight line at a constant speed of 50 mi/hr. Determine how fast is the distance between them changing after one second. 3. A sand is pouring from a spout at the rate of 25 cc/s. It froms a cone whose height is always 1/3 the radius of its base. At what rate is the height increasing when the cone is 50 cm high? 4. A cylindrical tank of radius 10 feet is being filled with water at a rate of 314 cubic feet per minute. How fast is the depth of water increasing? 5. A balloon is being inflated by pumped air at the rate of 2 cubic inches per second. How fast is the diameter of the balloon increasing when the radius is % inch?Maxima/Minima Problems 1. A rectangular field is to be fenced off along a straight river. If no fencing is needed along the river, show that the least amount of fencing will be required when the length of the field is twice its width. 2. Find the shape of the largest rectangle that can be inscribed in a given circle. 3. Divide the number 60 into two parts so that the product P of one part and the square of the other is maximum. 4. What is the maximum volume of a box that is constructed from a piece of cardboard 16 inches square by cutting equal squares out of the corners and turning up the sides? 5. A square sheet of galvanized iron, 100 cm x 100 cm will be used in making an open top container by cutting a small square from each corner and bending up the sides. Determine how large the square should be cut from each corner in order to obtain the largest possible volume.8. Assignment 2 Solve items 1-6 (Related Rates) and Illustrate items 1-5 (Maxima/Minima) Click here to submit