You have a cylinder with a diameter of 15 inches and a height of 12 inches. What is the volume of the largest sphere thg will fit inside it? If you can will you please show your work somehow?

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Well, there are two cases in here: 1. The cylinder is at least the same height as its base diameter. The sphere will have the same diameter, which is 2r. 2. The cylinder is short, the height is strictly less than the base diameter. We will denote [latex]r=\frac{h}{2}[/latex]. The volume is [latex]\frac{4}{3} \pi r^{3}[/latex]

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