Related Rates Cone

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the height of the water changing when the water is 2 ft deep?

• -9/(8pi) ft/sec

• 9/(8pi) ft/sec

• -8/(9pi) ft/sec

• 8/(9pi) f/tsec

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The tank is completely full and needs to be drained. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec.  How fast is the radius changing when the water is 2 ft deep?

• 4/(3pi) ft/sec

• 3/(4pi)ft/sec

• -3/(4pi) ft/sec

• -4/(3pi) ft/sec

Devin set up a toy rocket. For safety, he stands 6 meters from the rocket. He sets off the rocket and it heads straight up at a constant rate of 4 m/s.  How fast is the angle from Devin’s feet to the rocket changing after 2 seconds?

• 53.13 deg/sec

• -53.13 deg/sec

• .96 deg/s

• -.96 deg/sec

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

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.

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

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. What formula would you take the derivative of to solve this problem?

• V=(1/3)πr²h

• V=(4/3)πr³

• d=√(x²+y²)

• S=2lh+2lw+2hw

The volume of a cone of radius r and height h is given by v = (1/3) π r² h. If the radius and the height both increase at a constant rate of 1/2 centimeter per second, at what rate, in cubic centimeters per second, is the volume increasing when the height is 9 centimeters and the radius is 6 centimeters?

• 10π

• 24π

• 54π

• 108π

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec. When asked to find how fast the height of the water is changing when the water is 2 ft deep, what formula will we differentiate with respect to time?

• The Pythagorean Theorem

• The surface area of a cone

• The volume of a cone

• The height of a balloon

A water tank, shaped like an inverted circular cone, has a base radius of 6 ft and a height of 9 ft. The valve is opened and the water begins to decrease at a rate of 2 ft³/sec. Which of these are correct statements? Check all that are true.