SOLUTION: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a sphere with a radius of 70 cm.

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Question 862881: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a sphere with a radius of 70 cm.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Use the positive x axis for radius and the positive y axis for height.
V=y%2Api%2Ax%5E2. The description is of the cross section through the middle of the cylinder. This cross section uses a circle x%5E2%2By%5E2=70%5E2. You can reform the volume either in terms of x or in terms of y.

V=y%2Api%2A%2870%5E2-y%5E2%29%5E2
V=y%2Api%2A%2824010000-2%2A4900y%5E2%2By%5E4%29
highlight_green%28V=pi%2A24010000y-9600%2Api%2Ay%5E3%2Bpi%2Ay%5E5%29
Two choices. Use a graphing tool or try derivative of V and maybe then resort to a graphing tool. Where is derivative equal to zero? Corresponding x? Corresponding volume?

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potentially posting and keeping unfinished.