Question

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.

Answer #1

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you**

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

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

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.)

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

Determine the largest possible area for a rectangle that can be
inscribed in a circle of radius 7.8 cm.

Prove that a rectangular box of given volume inscribed in a
sphere of radius r is a cube.

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?).

The sphere is the shape with the smallest surface for a given
volume. to prove this statement properly requires variational
analysis. here we want to confirm this result only for a selection
of highly symmetric shapes by calculating the ratio of surface to
volume. find these ratios for each of these shapes. sphere,
cylinder, cube,pyramid, tetrahedron, cone. does this statement hold
for six shapes?

What is the area of the largest rectangle which can be inscribed
in the ellipse given by x^2/16 + y^2/4 = 1?

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.

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