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Implicit relationships in mathematics and physics describe complex interdependencies between variables, often representing them in equations where variables are not isolated. These relationships are key in understanding phenomena like gas behavior and electrical circuits, where changes in one variable affect others.

Solids of revolution involve creating 3D shapes by rotating a 2D curve around an axis. Calculated using integral calculus, they’re key in engineering and physics for determining volumes of complex objects, offering insight into real-world geometric shapes through mathematical principles.

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