Multiple choice

A right circular cone of the largest volume is cut out from a solid wooden hemisphere. The remaining material is what percentage of the volume of the original hemisphere?

  1. 50%

  2. 33.34%

  3. 75%

  4. 66.67%
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A Correct answer
Explanation

The largest cone cut from a hemisphere has its vertex at the center and base on the circular face. For a hemisphere of radius R, this cone has height R and base radius R. Volume of hemisphere is 2/3 πR³, cone volume is 1/3 πR³. Remaining material is 1/3 πR³, which is 50% of the hemisphere's volume.

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