Engineering Board Exam Reviewer · Optimization (Maxima and Minima) · hard
A right circular cone is inscribed in a sphere of radius R. For what ratio h/R of the cone's height to the sphere's radius is the cone's volume a maximum?
- 4/3
- 3/2
- 2
- 1
Answer
A. 4/3
Solution
The base radius r satisfies r2=h(2R-h), so V= π3r2h= π3h2(2R-h). V'= π3(4Rh-3h2)=0 h=4R/3. The ratio is 43.
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