Question

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?

Answer #1

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.

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?

a
cone with a radius of 5 ft and height 8 ft is leaking 2 cubic feet
of water per second how fast is the radius of the surface of the
water decreasing when the depth of the water is 4 ft

Suppose Aaron is pumping water into tank, shaped like an
inverted circular cone, at a rate of 1600ft^3/min. If the altitude
of the cone is 10ft and the radius of the base of the cone is 5ft,
find the rate at which the radius of the liquid is changing when
the height of the liquid is 7ft.

Consider the following container. It is a cut cone with a top
radius of 7 ft and a bottom radius of 3 ft. It has a height of 12
ft and water (density 62.5 lb/ft^3) is currently in the container
to a depth of 5 ft. There is a spout on this container at the
top.
Write down but DO NOT EVALUATE an integral to find the work
necessary to pump all the water in this container up out of...

A tank, shaped like a cone has height 99 meter and base radius
11 meter. It is placed so that the circular part is upward. It is
full of water, and we have to pump it all out by a pipe that is
always leveled at the surface of the water. Assume that a cubic
meter of water weighs 10000N, i.e. the density of water is
10000Nm^3. How much work does it require to pump all water out of
the...

A paper cup in the shape of a cone with height 5 cm and radius 3
cm with the point of the cone at the bottom. A small leak develops
in the cup causing water to leak out at a rate of 0.1
cm3/s. Find the rate at which the height of the water in
the cup changes when the depth of the water is 2 cm. Recall that
the volume of a cone is v=1/3(pi)(r2)h

The height of water in a small tank shaped as a right-circular
cone (cf. a filter funnel) is changing at 4.25 cm/min. The flow
rate of water into the tank is 1.25 kg/s, while the flow rate out
is 1.15 kg/s. The height of the tank is 65.0 cm and its diameter is
75.0 cm. What is the water level within the tank?

The radius of a circular cylinder is increasing at rate of 3
cm/s while the height is decreasing at a rate of 4 cm/s.
a.) How fast is the surface area of the cylinder changing when
the radius is 11 cm and the height is 7 cm? (use A =2 pi r2 +2 pi
rh )
b.) Based on your work and answer from part (a),is the surface
area increasing or decreasing at the same moment in time? How do...

related rates
An upside down cone is being emptied at the rate of 4 cubic feet
per second. The height of the cone is 20 feet and the radius is 6
feet. Find the rate of the change of water level when the depth is
12 feet.
List any restrictions if any involving this related rates
question...?
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