Question

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
cm^{3}/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)(r^{2})h

Answer #1

The diagram shows a toy. The shape of the toy is a cone, with
radius 4 cm and height 9 cm, on top of a hemisphere with radius 4
cm. Calculate the volume of the toy. Give your answer correct to
the nearest cubic centimetre. [The volume, V, of a cone with radius
r and height h is V = 3 1 πr 2h.] [The volume, V, of a sphere with
radius r is V = 3 4 πr 3.]

a recreational lake created by an artificial damn has
the shape of a truncated cone. if the depth of water in the lake
(h) is 0 the radius of the lake would be r_1= 300meters. the radius
of the lake at it's surface is given in terms of the lake's depth
via the following relation r_2 = 300 + h.
a) given that the volume of a truncated cone is given
by the formula pi/3 × h(r(2/1)+ r(2/2) + r...

A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 550 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.03 cents per square centimeter. The top will be made of glued
paper, costing 0.07 cents per square centimeter. Find the
dimensions for the package that will minimize production cost.
Helpful information: h : height of cylinder, r : radius of cylinder
Volume of a cylinder: V...

The radius of a cone is decreasing at a constant rate of 5
centimeters per minute, and the volume is decreasing at a rate of
148 cubic centimeters per minute. At the instant when the radius of
the cone is 22 centimeters and the volume is 21 cubic centimeters,
what is the rate of change of the height? The volume of a cone can
be found with the equation V=1/3 pi r^2h. Round your answer to
three decimal places.

A microwaveable cup-of-soup package needs to be constructed in
the shape of cylinder to hold 250 cubic centimeters of soup. The
sides and bottom of the container will be made of styrofoam costing
0.03 cents per square centimeter. The top will be made of glued
paper, costing 0.07 cents per square centimeter. Find the
dimensions for the package that will minimize production
cost.
Helpful information:
h : height of cylinder, r : radius of
cylinder
Volume of a cylinder: V=πr2hV=πr2h...

1) A cylindrical tank with a radius of 10 feet and a height of
20 feet is leaking. An observer notices that the height of the tank
is goinf down at a constant rate of 1 foot per second. At what rate
is the water leaking our of the rank (measured in volume) when the
height of the water is 5 feet? The colume of a cylinder of height h
and radius is V=pi*r2*h.
a. -314
b. - 1,245
c....

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...

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?

10. A circular cylinder with a radius R of 1 cm and a
height H of 2 cm carries a charge density of ρV = H r2 sin φ µC/cm3
(r is a point on the z-axis, φ is an azimuthal angle). The cylinder
is then placed on the xy plane with its axis the same as the
z-axis. Find the electric field intensity E and the electric
potential V on point A on z-axis 2 cm from the top...

URGENT PLEASEEE
ASAP!!!
A pool is circular with a diameter of 5 meters. Depth is constant along the east-west lines and increases linearly from 0.5 meter at the south end to 2 meters at the north end. Determine the volume of the water in the pool.
(b) A bit of radius r1 = 1 cm is used to drill a sphere of radius r2 = 4 cm.
Find the remaining ring-shaped volume, given that the volume of a sphere of...

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