The 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=2πr
A=πr²
V=(4/3)πr³
S=4πr²
2. Multiple Choice
3 minutes
1 pt
All 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*w
V=3s²
A=s²
V=s³
3. Multiple Choice
3 minutes
1 pt
In 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=πr²h
V=(πr²h)/3
V=(4/3)πr³
4. Multiple Choice
3 minutes
1 pt
A 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)πr²h
V=(4/3)πr³
d=√(x²+y²)
S=2lh+2lw+2hw
5. Multiple Choice
3 minutes
1 pt
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=c²
d=√(x²+y²)
h=r⋅sinθ
1=sin²θ+cos²θ
6. Multiple Choice
3 minutes
1 pt
A 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=tanθ
r=cos(12)
ax²+bx+c=0
a²+b²=c²
7. Multiple Choice
3 minutes
1 pt
A 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/secθ
a²+b²=c²
V=(4/3)πr³
It depends on if the winch is man operated or not.
8. Multiple Choice
3 minutes
1 pt
A 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?