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Maximizing Cylinder Volume

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Maximizing Cylinder Volume, a selection of answers from the Dr. Math archives.

Cylinder Formulas - Dr. Math FAQ
A cylinder is a surface generated by a family of all lines parallel to a given line (the generatrix) and passing through a curve in a plane (the directrix). A right section is the curve formed by the intersection of the surface and a plane perpendicular to the generatrix. The parallel bases of a cylinder may form any angle with the axis.

More commonly, a cylinder includes the solid enclosed by a cylinder and two parallel planes. The region of either of the parallel planes enclosed by the surface is called a base of the cylinder. The perpendicular distance between the planes of the bases is the height of the cylinder. The line segment cut on any of the generating lines by the two parallel planes is called a lateral edge.

From the archives:

Cylinder Height, Area, Volume
Why does the volume of a cylinder get larger as the radius gets larger and the height gets smaller?

Cylinder Volume and Surface Area
How does one make a cylinder that holds the greatest volume if the entire surface area is 600 cm squared?

Cylinder Problem
Is it possible to construct two cans with different volumes but the same surface area?

Maximizing the Volume of a Cylinder
I need to maximize the volume of a right-circular cylinder that fits inside a sphere of radius 1 m.

Applied Max/Min Problems
Find the largest possible volume of a right circular cylinder that is inscribed in a sphere of radius r.

Maximizing the Volume of a Cylinder
Find the dimensions of the cylinder of maximum volume that can be inscribed in a cone having a diameter of 40 cm and a height of 30 cm. Show that the maximum area of the cylinder is 4/9 the volume of the cone.

Oil Can Dimensions
What are the dimensions of an oil can with a one-liter capacity that uses the least amount of tin?

Calculus: Rate of Change in Volume
The radius of a right circular cylinder is decreasing at the rate of 4 feet per minute, while the height is increasing at the rate of 2 feet per minute. Find the rate of change in the volume when the radius is 2 feet and the height is 6 feet.

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