Deriving the Equation for Finding the Area of a Sphere

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I have a series of questions that are all, I believe, leading up to finding the formula for finding the formula for calculating the area of a sphere (the last question of the series makes me imply that). enter image description here

I am not able to understand the given situation because of the way the question is phrased. I would appreciate it if anyone can guide me through this process. I understand that these questions are based on one another so if someone can help me with one, or two, of the questions then I hope to complete the rest of them.