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# Maximizing Volume of a Cylinder, Given Lateral Area

Directions: Find at least 3 possible measures for the height and the radius of a cylinder with a lateral area of 144pi square centimeters.

Which of your dimensions will give you the largest volume?

### Hint

How can we use the given lateral area to find the dimensions of the cylinder? How does increasing/decreasing the radius or height affect the volume?

If you limit the dimensions to whole numbers, the dimensions that maximize the volume is radius is 72 and the height is 1. If you do not limit the dimensions, there is theoretically no limit to the maximum because the height could be infinitely small, which makes the radius infinitely large, which continues to increase the volume infinitely.

Source: Jason Miller

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