Question

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 you know?

Answer #1

The radius of a cylinder is increasing at a rate of 3cm/min
while the height is decreasing at a rate of 10cm/min. What is the
rate of change of the volume of the cylinder when the height is
100cm and the radius is 20cm?
Please solve the question step by step

The side x of a rectangle is increasing at a rate of 2 cm/s
while its side y is decreasing
at a rate of 1 cm/s.
(a) Find how fast the perimeter P of the rectangle is changing when
x = 4 cm and
y = 3 cm.
(b) Find how fast the area A of the rectangle is changing when x =
4 cm and y = 3
cm.
(c) Find how fast the length l of diagonal of...

The altitude (height) of a triangle is increasing at a rate of 1
cm/min while the area of the triangle is increasing at a rate of 2
square cm per min. At what rate is the base of the triangle
changing when the altitude is 10 cm and the area is 100 square
cm?

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...

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.

The height of a triangle is decreasing at a rate of 1 cm/min
while its area is increasing at a rate of 2 cm^2/min.
(a) What is the base of the triangle when its height is 10 cm
and its area is 100 cm^2?
(b) At what rate is the base of the triangle changing when its
height is 10 cm and its area is 100cm^2?

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...

The altitude (i.e., height) of a triangle is increasing at a
rate of 1.5 cm/minute while the area of the triangle is increasing
at a rate of 2.5 square cm/minute. At what rate is the base of the
triangle changing when the altitude is 11.5 centimeters and the
area is 87 square centimeters?

A circular cylinder with a radius R of 1 cm and a height H of 2
cm carries a charge density of pv = h R^2 uC/cm^3 (h is a point on
the z-axis). 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 and the electric potential V on point A on z-axis 2 cm from the
top of the cylinder.

A potter forms a piece of clay into a right circular cylinder.
As she rolls it, the height hh of the cylinder increases and the
radius r decreases. Assume that no clay is lost in the process.
Suppose the height of the cylinder is increasing by 0.4 centimeters
per second. What is the rate at which the radius is changing when
the radius is 4 centimeters and the height is 11 centimeters?

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