Name:    03-04 - Related Rates

Multiple Choice
Identify the choice that best completes the statement or answers the question.

1.

Consider the following relationship exists between y and x over time, t :

Determine   at the moment that  ,   , and

 a. d. b. e. c. f.

2.

 A fish aquarium in the shape of a rectangular prism cracked near the bottom of the tank.  Water is pouring out at a rate of  . The dimensions of the aquarium tank are: What is the rate at which the water level is decreasing?
 a. d. b. e. c. f.

3.

 A 12 foot ladder is leaning against a wall and top of the ladder begins to slide down the wall.  Let the height the ladder reaches up the wall be the variable x in feet and the distance the foot of the ladder is horizontally away from the bottom of the wall be the variable y in feet.At the moment the value of  x = 10 feet, the velocity of the top of the ladder is falling at is .  Determine the approximate speed at which the foot of the ladder is moving (i.e. find ).
 a. d. b. e. c. f.

4.

 A consumer researcher noticed that a particular brand of soap is roughly a rectangular prism and reduced in size as it was used in a specific ratio of  height, length, and width to respectively . If this ratio remains consistent and the volume of the bar of soap is decreasing at a rate of , determine the rate at which the height is decreasing when the bar of soap has the dimensions.
 a. d. b. e. c. f.

5.

 A sink is approximately the shape of a hemisphere with a diameter of 32 cm, as shown in the diagram, and is filling from the bottom up.  The volume of the water can be described as a function of the height of the water using the function:If the faucet is filling the sink at a rate of , how fast is the level of water rising when the height is 6 cm?
 a. d. b. e. c. f.

6.

 Water is being pumped in to a trough at 3 ft3/min. The trough is a triangular prism that is 10 feet long. The ends or bases of the trough are isosceles triangles. The isosceles triangles have a base of 6 feet and 4 feet high as shown in the diagram.How fast is the height of the water level rising when the water is 3 feet high?
 a. d. b. e. c. f.