Engineering Board Exam Reviewer · Solid Geometry: Cones, Spheres, and Frustums · hard
Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 6.
- 301.59
- 226.19
- 268.08
- 150.8
Answer
C. 268.08
Solution
For a cone of height h in a sphere of radius R, the base radius satisfies r2=h(2R-h). V= π3h2(12-h) is maximized at h=8, giving V= π3(64)(4)=256π/3 268.08.
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