Question

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

Answer #1

A circular cone is 10 cm wide at the base and has a slant height
of 8.5 cm. Determine:
a. Volume of the cone =
b. Total surface area of the cone =
c. The angle the slant height makes with the base diameter =
d. The cylinder shown here has the same height and base radius
as the cone, by what percent the volume of
the cylinder exceeds the volume of the cone?

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.

2. A cylinder is inscribed in a right-circular cone of altitude
12cm, and a base with radius of 4cm. Find the dimensions of the
cylinder that will make the total surface area a maximum.

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.

1) Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis. ?=2?^(1/2), y=x about
y=6 (Use symbolic notation and fractions where needed.)
2) Find the volume of a solid obtained by rotating the region
enclosed by the graphs of ?=?^(−?), y=1−e^(−x), and x=0 about
y=4.5.
(Use symbolic notation and fractions where needed.)

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

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 right-circular cylinder with volume of V 3 m is to be
constructed. Find the dimensions that will minimize the surface
area.

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

Use
Lagrange multipliers to find the dimensions of a right circular
cylinder with volume Vo cubic units and minimum surface area.
r(Vo)=
h(Vo)=
Thank you!

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