Question

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.

Answer #1

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The radius of a melting snowball is decreasing at a rate of 10
centimeters per minute. How fast is the volume changing when the
radius is 1 /2 centimeters? (Feel free to leave your answer in
terms of π, you don’t need to use the approximation π ≈ 3.14).

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.]

The
radius of a right circular cone is decreasing at a rate of
1.5cm/sec and the height is increasing at a rate of 5cm/sec. At
what rate is the volume changing when the height is 12cm and the
radius 2cm? Leave your answer in terms of pi.

Gravel is being dumped from a conveyor belt at a rate of 30
cubic feet per minute. It forms a pile in the shape of a right
circular cone whose base diameter and height are always equal. How
fast is the height of the pile increasing when the pile is 22 feet
high? Recall that the volume of a right circular cone with height h
and radius of the base r is given by V = 1/3πr^2h

When air expands adiabatically (without gaining or losing heat),
its pressure P and volume V are related by the
equation PV^1.4=C where C is a
constant. Suppose that at a certain instant the volume is 440 cubic
centimeters and the pressure is 93 kPa and is decreasing at a rate
of 7 kPa/minute. At what rate in cubic centimeters per minute is
the volume increasing at this instant?

When air expands adiabatically (without gaining or losing heat),
its pressure PP and volume VV are related by the equation
PV1.4=CPV1.4=C where CC is a constant. Suppose that at a certain
instant the volume is 680680 cubic centimeters and the pressure is
8787 kPa and is decreasing at a rate of 1515 kPa/minute. At what
rate in cubic centimeters per minute is the volume increasing at
this instant?

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

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...

As a large cube of ice melts at a rate of 5 cubic inches per
minute, it maintains its cubical shape. Find the rate of change of
the length of the side of the ice cube at the instant when the side
length is 10 inches.

As a large cube of ice melts at a rate of 5 cubic inches per
minute, it maintains its cubical shape. Find the rate of change of
the length of the side of the ice cube at the instant when the side
length is 10 inches.

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