Answers included! Looking for some help on this work sheet!

A kite is flying at a height of 40 m. The boy who is flying this kite is running horizontally at 3 m/s and is letting out the string so that the length of the string is increasing. Find this rate when the length of the string is 50 m. [9/5 m/s] A spherical balloon is being inflated so that its volume is increasing at the rate of 5 m /min. At what rate is the diameter increasing when the radius is 6 m? [5/72n m/min] 3. A spherical snowball is being made so that its volume is increasing at the rate of 8 m'/min. Find the rate at which the radius is increasing when the snowball is 4 m in diameter. [1/2n m/min] 4. Sand is being dropped at the rate of 10 fi'/min into a conical pile. If the height of the pile is always twice the base radius, at what rate is the height increasing when the pile is 8 ft high? [5/8, ft/min] 5. A light is hung 15 m above a straight horizontal path. If a man 2 m tall is walking away from the light at a rate of 2 m/s, how fast is his shadow lengthening? [4/13 m/s] 6. A man 6 ft tall is walking towards a building at the rate of 5 fus. If there is a light on the ground 50 ft from the building, how fast is the man's shadow on the building growing shorter at the moment he is 30 ft from the building? [15/4 fu/s] 7. A water tank in the shape of an inverted cone is being emptied at the rate of 6 m'/min. If the height of the cone is 24 m and the base radius is 12 m, how fast is the water level going down when the depth of the water is 10 m? [6/2511 m/min] 8. A trough is 12 m long and its ends are in the form of inverted isosceles triangles with height 3 m and base 3 m. If water is flowing into the trough at the rate of 2 m'/min, how fast is the water level rising when the water is I m deep? [1/6 m/min]