WorksheetsRelated Rates
Total questions: 8
Worksheet time: 24mins
Name
Class
Date
1.
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.
a)
C=2πr
b)
A=πr²
c)
V=(4/3)πr³
d)
S=4πr²
2.
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)
A=l*w
b)
V=3s²
c)
A=s²
d)
V=s³
3.
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.
a)
S=πr√(r^2+h^2)
b)
V=πr²h
c)
V=(πr²h)/3
d)
V=(4/3)πr³
4.
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.
a)
V=(1/3)πr²h
b)
V=(4/3)πr³
c)
d=√(x²+y²)
d)
S=2lh+2lw+2hw
5.
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?
a)
a²+b²=c²
b)
d=√(x²+y²)
c)
h=r⋅sinθ
d)
1=sin²θ+cos²θ
6.
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.
a)
h=tanθ
b)
r=cos(12)
c)
ax²+bx+c=0
d)
a²+b²=c²
7.
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.
a)
cosθ=1/secθ
b)
a²+b²=c²
c)
V=(4/3)πr³
d)
It depends on if the winch is man operated or not.
8.
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?
a)
o=a tanθ
b)
a=o tanθ
c)
o=h sinθ
d)
a=h cosθ
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