Question

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.

Answer #1

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.

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 cylinder is inscribed in a right circular cone of height 2.5
and radius (at the base) equal to 6.5. What are the dimensions of
such a cylinder which has maximum volume?
Asking for both radius and height.

The volume of a right circular cylinder is given by V=
πr2h, where r is the radius of its circular
base and h is its height.
Differentiate the volume formula with respect to t to determine
an equation relating the rates of change dV/dt , dr/dt ,
dh/dt.
At a certain instant, the height is 6 inches and increasing at
1 in/sec and the radius is 10 inches and decreasing at 1 in/sec.
How fast is the volume changing at...

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.

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).

Find the dimensions of the right circular cone of maximum volume
having a slant height of a=20 ft.
(Use symbolic notation and fractions where needed.)
radius = ? ft
height = ? ft

The radius and the height of a circular cone was measured and
found to be 10 cm and 30 cm with possible errors in measurement of
at most 0.1 cm and 0.05 cm respectively. What is the largest
possible error in using these values to compute the volume of the
cone?

Suppose the radius, height and volume of a right circular
cylinder are denoted as r, h, and V . The radius and height of this
cylinder are increasing as a function of time. If dr/dt = 2 and
dV/dt = 10π when r = 1, h = 2, what is the value of dh/dt at this
time?

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?

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