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 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 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 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?

Water is being pumped in to a trough
at 3 ft^{3}/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?