1. A 50-cm high trough filled with liquid is 200 cm long and has a cross-section of an isosceles trapezoid 30 cm wide at the bottom and 60 cm wide at the top. If the trough leaks water at the rate of 2000 cm /min, how fast in cm/min is the water level decreasing when the water is 20 cm deep? 2. Water is being poured into a spherical bowl of radius 4 cm at a rate of 2 cm /s. How fast is the water level rising when it is at 2 cm? Hint: The volume of a hemispherical bowl of radius R when V=> (3R->) the height of the water is y is: 3. Airplane A is 500 km south of airplane B. Plane A is flying 600 km/h going south while plane B is flying 800 km/h going west. If the two planes are of the same altitude, how fast is the distance between them changing at any time? 4. A man is walking beside a 30-m street lamp. After walking 25 m away from the street lamp, he sunk into a quicksand. At the time when 2 m of him are above the ground, he is sinking at I m/s. At what rate is the length of his shadow changing at that moment? 5. A spherical balloon is inflated so that its volume is increasing at the rate of 2 m /min. At what rate is the diameter increasing when the diameter is 6 m