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?


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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  1. what an awesome question. thank you!

  2. Did this with middle level kids today. The discussions, ways to problem solve, patterns, and conversations that came out of this were awesome!!! Used a Padlet for students to share answers. “We have the same numbers but his are switched with radius and height. Does that matter?” “Why does that work?”

    Another student made a table and looked for patterns. Another tried to find the largest radius that his calculator could fit and still keep the same lateral area. Pure awesomeness.

    • Robert Kaplinsky

      Thank you so much for sharing this Stacy. It certainly validates the work we’re all doing to share these problems with you.

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