When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation PVI'4 = C where C is a constant. Suppose that at a certain instant the volume is 660 cubic centimeters and the pressure is 83 kPa and is decreasing at a rate of 14 kPa/ minute. At what rate in cubic centimeters per minute is the volume increasing at this instant? \"\"3 min (Pa stands for Pascal -- it is equivalent to one Newton! (meter squared); kPa is a kiloPascal or 1000 Pascals. ) Sand is pouring out of a pipe and is forming a conical pile on the ground. 1 incoming sand The radius of the pile is increasing at a rate of 2 meters per day. conical The height is always 5 of the radius. When the pile has a radius of 16 meters, a) the Volume is [:] cubic meters b) the rate of change of the VOLUME is C] cubic meters per day.. Write your answers as decimal numbers rounded to 2 decimal places. Volume: %n (radius)2 height A police car is located 50 feet on a small straight road perpendicular to main highway. A red car is driving along a highway in the direction of an intersection with that small road and is 170 feet away from the intersection. The police radar reads that the distance between the police car and the red car (this distance is straight between them - not on either road) is decreasing at a rate of 95 feet per second. How fast is the red car actually traveling along the road? The actual speed (along the road) of the red car is [j feet per second Police Water is leaking out of an inverted conical tank at a rate of 8300 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 6 meters and the diameter at the top is 4.5 meters. If the water level is rising at a rate of 22 centimeters per minute when the height of the water is 2 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute. Recall that the volume of a right circular cone with height h and radius of the base r is given by 1 V = 1r'r2h 3