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- 1. Multiple ChoiceThe radius r of a sphere is increasing at a rate of 2 inches per minute. Find the rate of change of the volume when r=6 inches.C=2πrA=πr²V=(4/3)πr³S=4πr²
- 2. Multiple ChoiceAll edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing each edge is 1 centimeter.A=l*wV=3s²A=s²V=s³
- 3. Multiple ChoiceIn a cone, find the rate of change of the volume if dr/dt is 2 inches per minute and the height is 3r when the radius is 6.S=πr√(r^2+h^2)V=πr²hV=(πr²h)/3V=(4/3)πr³
- 4. Multiple ChoiceA conical tank is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rate of 10 cubic feet per minute, find the rate of change of the depth of the water when the water if 8 feet deep.V=(1/3)πr²hV=(4/3)πr³d=√(x²+y²)S=2lh+2lw+2hw
- 5. Multiple Choice
A construction worker pulls a five meter plank up the side of a building under construction by means of a rope tied to one end of the plank. Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of .15 meters per second. How fast is the end of the plank sliding along the ground when when it is 2.5 meters from the wall of the building?a²+b²=c²d=√(x²+y²)h=r⋅sinθ1=sin²θ+cos²θ - 6. Multiple ChoiceA boat is being pulled into dock by means of a winch 12 feet above the deck of the boat. The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out.h=tanθr=cos(12)ax²+bx+c=0a²+b²=c²
- 7. Multiple ChoiceA boat is being pulled into dock by means of a winch 12 feet above the deck of the boat. Suppose the boat is moving at a constant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when there is a total of 13 feet of rope out.cosθ=1/secθa²+b²=c²V=(4/3)πr³It depends on if the winch is man operated or not.
- 8. Multiple ChoiceA fish is reeled in at a rate of 1 foot per second from a point 10 feet above the water. At what rate is the angle between the line and the water changing when there is a total of 25 feet of line out?o=a tanθa=o tanθo=h sinθa=h cosθ
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