Word problems finding a lot of cm^3/mix&max as well as some other things :)

Question

1.A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. At what rate is the volume of the snowball decreasing when the radius is 9 cm. (Note the answer is a positive number).

 ? =  cm^3/min

Hint: The volume of a sphere of radius r is V=4/3 pir^3

2.A street light is at the top of a 20 ft tall pole. A woman 6 ft tall walks away from the pole with a speed of 8 ft/sec along a straight path. How fast is the tip of her shadow moving when she is 50 ft from the base of the pole?

? ft/sec

3.Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 13 feet high?

Recall that the volume of a right circular cone with height h and radius of the base r is given by V=1/3 pir^2ℎ

? ft/min

4.When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PV^1.4=C where C is a constant. Suppose that at a certain instant the volume is 650 cubic centimeters and the pressure is 83 kPa and is decreasing at a rate of 11 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?

  ? cm^3/min

(Pa stands for Pascal -- it is equivalent to one Newton/(meter squared); kPa is a kiloPascal or 1000 Pascals.)

5.Water is leaking out of an inverted conical tank at a rate of 7700 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 13 meters and the diameter at the top is 3 meters. If the water level is rising at a rate of 22 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

 ? cm^3/min

6.At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 25 knots and ship B is sailing north at 25 knots. How fast (in knots) is the distance between the ships changing at 3 PM? (Note: 1 knot is a speed of 1 nautical mile per hour.)

 ?  knots

   

   

Answer 1