Question: NASA will return to the moon under the Artemis program, utilizing the recently developed Space Launch System (SLS) rocket (link). The SLS is the world's

NASA will return to the moon under the Artemis program, utilizing the recently developed Space Launch System (SLS) rocket (link). The SLS is the world's most powerful rocket, consisting of two solid rocket boosters mounted alongside a central core rocket, which produce a combined 8.8 million pounds of thrust.

The central core is cylindrical in shape and stores liquid hydrogen and oxygen to fuel the four RS-25 rocket engines mounted on the bottom. We can model the fuel storage compartment of the SLS system as a cylinder of height H and radius R (or diameter D), as shown in the figure below. To satisfy launchpad requirements, the central core dimensions must satisfy the requirement that the sum of the Height plus 10 times the Diameter should equal 140 meters. What dimensions H and D produce a central core of the SLS with the largest volume storage capacity? What is the volume in m3?

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