Related Rates

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

Tags

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.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.

• S=πr√(r^2+h^2)
• V=πr²h
• V=(πr²h)/3
• V=(4/3)πr³

Tags

CCSS.HSG.GMD.A.1

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSG.GMD.A.3

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

Tags

CCSS.HSA.CED.A.2

CCSS.HSG.SRT.C.6

CCSS.HSG.SRT.C.8

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

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.8.G.B.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?

• o=a tanθ
• a=o tanθ
• o=h sinθ
• a=h cosθ

Tags

CCSS.8.EE.C.7B