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curve surface area
A parabola is a two dimensional open curve. Its area is therefore infinite.
Yes.
theorems relating respectively to the volume and the surface area of a solid generated by the revolution of plane figure around an axis lying in the same plane. 1. when a plane figure is revolved about an axis lying in the same plane (but not cutting the area)The volume generated is equal to the product of the area and the length of the path described by the centre of gravity of the area . 2. When a plane curve is revolved about an axis lying in the same plane (but not cutting the curve) the surface area generated is equal to the product of the length of the curve and the length of the path of the centre of gravity of the curve.
Mass does not directly affect surface area. Surface area is a measure of the total area of an object's external surfaces, while mass is a measure of the amount of matter in an object. However, as the mass of an object increases, its volume typically increases as well, which can indirectly affect its surface area if the shape remains constant. Objects with larger masses may have larger surface areas if their volume increases proportionally.