derivation of center of mass of solid cone
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The center of mass of a cone is located along a line. This line is perpendicular to the base and reaches the apex. The center of mass is a distance 3/4 of the height of the cone with respect to the apex. This means the center of mass is 1/4 of the height from the base.
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The center of mass is a distance 3/4 of the height of the cone with respect to the apex. This means the center of mass is 1/4 of the height from the base. This confirms the assumption based on the shape of the cone: the center of mass is closer to the base than to the apex.
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