Question

A liquid is poured into a conical container with a base radius of 6 inches and a height of 6 inches. When the water is 3 inches deep it is increasing at a rate of 4 inches/min. What rate is the lateral surface area of the water changing when the depth is 3 inches?

Answer #1

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Water is poured into a conical container with height 4 in. and
base radius 4 in. When the height of the water in the container is
2.5 inches it is increasing at 3 in/min. At what rate is the
lateral surface area of the water changing when the height is 2.5
inches? The formula for the lateral surface area of the cone is
Slateral = πrs where s is the slant or lateral length.

Water is being poured into a cone-shaped container with radius 4
inches, and height 4 inches. When the depth of the water is 3
inches, it is increasing by 3in/min. At what time, how fast is the
surface area, A, that is covered by water increasing?

Water flows into a conical container at a rate of 5 m3/s. Assume
that the container has
a height of 4 meters and a base radius of 2 meters. Find the rate
at which the water
level is rising when the water is 2 meter deep.

a conical water tank with the vertex down has a radius of 9feet
at the top and is 23 feet high. If water flows into the tank at a
rate of 30ft^3/min, how fast is the depth of the water increasing
when the water is 17 feet deep? Include units

A conical water tank with vertex down has a radius of 14 feet at
the top and is 21 feet high. If water flows into the tank at a rate
of 20 ft^3/min, how fast is the depth of the water increasing when
the water is 13 feet deep?

A conical container of radius 6 ft and height 24 ft is filled to
a height of 22 ft with a liquid weighing 62.4 lb/ft3.
How much work will it take to pump the liquid to a level of 2 ft
above the cone's rim?

Suppose that liquid is to be cleared of sediment by allowing it
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radius of 4cm at the top. Suppose also that the liquid is forced
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depth of the liquid changing at the instant when the liquid in the
cone is 6cm deep ?

Corn is being poured through a chute at the rate of and falls
into a conical pile whose bottom radius is always the height. How
fast will the radius of the base change when the pile is 8 feet
high? Leave answer in
terms of pi

A conical paper cup 3 inches across the top and 4 inches deep is
full of water. The cup springs a leak at the bottom and loses water
at the rate of 2 cubic inches per minute. How fast is the water
level dropping at the instant when the water is exactly 3.5 inches
deep?

A conical container of radius 5ft and height 30ft is filled to a
height of 16ft of a liquid weighing 60.6 Ib/ft^3.
a. How much work will it take to pump the contents to the
rim?
b. How much work will it take to pump the liquid to a level of
4ft above the cone's rim?

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