Question

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

Answer #1

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.)

Please find the dimensions of the largest cylinder that can be
inscribed in a sphere with radius equal to rr.
Use optimization

If the cylinder of largest possible volume is
inscribed in a given sphere, determine the ratio of the
volume of the sphere to that of the cylinder.

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.

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

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 rectangular solid of largest volume
which can be inscribed in the ellipsoid
x2/16+y2/4+z2/9=1
Hint: Let (?, ?, ?) represent one of the eight vertices of the
solid. Then by symmetry the volume of the solid is ? =
(2?)(2?)(2?).

Find the area of the largest rectangle that can be inscribed in
a semicircle of radius r = 2.

Find the area of the largest trapezoid that can be inscribed in
a circle of radius 2 and whose base in as diameter of the
circle.

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

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