The greatest volume of a solid cone which can be cut off from a solid hemisphere of radius r unit is ______.
WBBSE
Class X
Mathematics
Sphere
01 Mark
2025
(2/3)πr³
Explanation:
- The largest cone that can be cut from a hemisphere is the one that fits perfectly inside it.
- The radius and height of this cone are both r.
- Volume of a cone is given by:
V = \frac{1}{3} \pi r^2 h
Substituting h = r:
V = \frac{1}{3} \pi r^2 \times r
V = \frac{1}{3} \pi r³
Since the largest cone inside the hemisphere occupies 2/3rd of its volume, we multiply by 2:
V = \frac{2}{3} \pi r³
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