Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · hard
A right circular cylinder is inscribed in a sphere of radius 6. Find the height of the cylinder that maximizes its volume.
- 4 3
- 6
- 3 3
- 8
Answer
A. 4 3
Solution
Let r = cylinder radius, h = height. From the sphere: r2+≤ft(h/2 )2=36 r2=36-h2/4. V=π r2h=π≤ft(36h-h3/4 ). V'=π≤ft(36-3h2/4 )=0 h2=48 h=4 3.
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