At what distance from the base is the center of gravity of a solid right circular cone of height h situated________________?
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Answer: D. h/4
Explanation
The center of gravity of a solid right circular cone of height h is situated at h/4 from its base. Integration of differential mass elements along the conical axis yields this exact geometric centroid location. This analytical result applies universally to any homogeneous solid right circular cone. Centroid calculations require integrating the first moment of volume over the entire geometric shape. For a hollow conical shell, the center of gravity is located higher up at one-third of the height. Symmetry ensures that the center of gravity lies directly on the central longitudinal axis of the cone.
Mechanical engineers use centroid locations to analyze stability and tipping moments for conical structures. Calculating centers of gravity is essential for balancing rotating machine components and hoppers. Physics and engineering curricula use solid cones as standard problems for integration practice. Height over two represents the midpoint of a cylinder or prism rather than a conical shape. Height over three is the center of gravity for a triangular area or a hollow conical shell. Other fractions like h/6 or three-fifths do not match the calculus integration results for solid cones.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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