Question

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.

Answer #1

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?

A tank in the shape of an inverted right circular cone has
height 9 meters and radius 13 meters. It is filled with 3 meters of
hot chocolate.
Find the work required to empty the tank by pumping the hot
chocolate over the top of the tank. Note: the density of hot
chocolate is δ=1480kg/m^3

A tank in the shape of an inverted right circular cone has
height 7 meters and radius 3 meters. It is filled with 6 meters of
hot chocolate. Find the work required to empty the tank by pumping
the hot chocolate over the top of the tank. The density of hot
chocolate is δ=1080 kg/m^3. Your answer must include the correct
units.

A tank in the shape of an inverted right circular cone has
height 88 meters and radius 1616 meters. It is filled with 22
meters of hot chocolate.
Find the work required to empty the tank by pumping the hot
chocolate over the top of the tank. Note: the density of hot
chocolate is δ=1450kg/m3

(Integration Application) A water tank is shaped like an
inverted cone with a height 2 meters and top radius 6 meters is
full of water. Set up a Riemann Sum and an Integral to model the
work that is required to pump the water to the level of the top of
the tank? No need to integrate here. (Note that density of water is
1000 kg/m3 ).
RIEMANN SUM ______________________________________________
INTEGRAL____________________________________________________
Provide an explanation as to the difference of the...

A tank in the shape of an inverted right circular cone has
height 6 meters and radius 2 meters. It is filled with 5 meters of
hot chocolate. Find the work required to empty the tank by pumping
the hot chocolate over the top of the tank. The density of hot
chocolate is \delta = 1090kg/m^3 Your answer must include the
correct units.

A tank in the shape of an inverted right circular cone has
height 7 meters and radius 3 meters. It is filled with 6 meters of
hot chocolate. Find the work required to empty the tank by pumping
the hot chocolate over the top of the tank. The density of hot
chocolate is δ=1080 kg/m^3. Your answer must include the correct
units.
NOTE: 112174.092J is incorrect?

A tank shaped like a cone pointing downward has height 9 feet
and base radius 3 feet, and is full of water. The weight density of
water is 62.4 lb/ft^3. Find the work required to pump all of the
water out over the top of the tank.

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 tank in shape of an inverted right circular cone has height 10
m and radius 10 m. it is filled with 7 m of hot chocolate. Find the
work required to empty the tank by bumping the hot chocolate over
the top. density of chocolate equal 1510kg/m^3

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