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

Question

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

1. A. 33.33%
2. B. 50% (Correct answer)
3. C. 75%
4. D. 66.66%

Correct Answer

Option B — 50%

Detailed Solution & Explanation

The correct answer is 50%.

Key Points

• Hemisphere volume = (2/3)*pi*r^3. Largest inscribed cone: h = r, base radius = r. Cone volume = (1/3)*pi*r^3. Remaining = (1/3)*pi*r^3. Percentage = (1/3)/(2/3) x 100 = 50%.