Question

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.

Answer #1

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.

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

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?

Find the volume of the largest right circular cylinder that can
be inscribed in a sphere of radius 4

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
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.

Find the circular cylinder of largest lateral area which can be
inscribed in a sphere of radius 4 feet. (Surface area of a cylinder
of radius r and height h is 2πrh.)

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

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?

what is the largest volume that a cone inscribed in a sphere of
radius 9 cm can have?

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